lesson 2 homework practice solve two step equations answer key

Two-Step Equations Exercises

Two-step equations practice problems with answers.

Hone your skills in solving two-step equations because it will serve as your foundation when solving multi-step equations. I prepared eight (8) two-step equations problems with complete solutions to get you rolling.

My advice is for you to solve them by hand using a pencil or pen and paper. Believe me, you get the most benefit from this exercise by doing it yourself first before looking at the solution set.

If by any chance you get stuck or don’t know what to do next, please feel free to review my other lesson about two-step equations. Click the link below to get there. Enjoy!

Solving Two-Step Equations

1) Solve the two-step equation for [latex]g[/latex].

[latex]2g – 4 = 6[/latex]

Add both sides by [latex]4[/latex] then divide both sides by [latex]2[/latex].

2) Solve the two-step equation for [latex]x[/latex].

[latex]2x + 15 = – 3x[/latex]

Subtract both sides by [latex]2x[/latex]. Finally, divide both sides of the equation by [latex]-5[/latex].

3) Solve the two-step equation for [latex]k[/latex].

[latex]{\Large{{k \over 4}}} – 7 = – 5[/latex]

Add both sides by [latex]7[/latex]; followed by multiplying both sides by [latex]4[/latex].

4) Solve the two-step equation for [latex]m[/latex].

[latex]{\Large{{{m + 9} \over 5}}} = {\large{2}}[/latex]

Multiply [latex]5[/latex] on both sides then subtract by [latex]9[/latex] on both sides of the equation as well.

5) Solve the equation for [latex]y[/latex].

[latex]0 = – 1 – y[/latex]

Add [latex]1[/latex] to both sides of the equation. Notice that the coefficient of [latex]-y[/latex] is [latex]-1[/latex]. That means, we should divide both sides by [latex]-1[/latex] to isolate and therefore solve for [latex]y[/latex].

6) Solve the equation for [latex]r[/latex].

[latex] – 3\left( {r – 7} \right) = – 24[/latex]

First, divide both sides of the equation by [latex]-3[/latex] then add by [latex]7[/latex].

7) Solve the equation for [latex]z[/latex].

[latex]{\Large{5 \over 4}}z + {\Large{3 \over 4}}z = 1[/latex]

8) Solve the equation for [latex]x[/latex].

[latex]4.25 – 0.25x = 3.75[/latex]

You may also be interested in these related math lessons or tutorials:

Multi-Step Equations Practice Problems with Answers

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Two Step Equations Worksheets

The first major leap forward for students in prealgebra is working with equations that require multiple steps to solve. When an equation is presented to you, it is balanced meaning that both sides are equal. You can easily rearrange any equation by simply performing the operation of your choice. You just need to make sure to process that operation on both sides of the equal symbol. Whatever you decide to do to one side, will be done to the other. In most cases we are simply trying to get a variable by itself and determine what it is equal to. The most commonly used variable is the letter “x”. These worksheets and lessons help students learn how to manage problems that involve solving equations in at least two steps.

Aligned Standard: 7.EE.B.3

• Solve For X Step-by-Step Lesson - Two thumbs up if you get this one. You get two either way!
• Guided Lesson - Play through on these. Make sure to get rid of the constant first.
• Guided Lesson Explanation - In some cases, I made two steps into three steps.
• Independent Practice - I used all numbers under 20 in the operations to make sure basic operations don't trip you up.
• Matching Worksheet - Find the value of the variables in all cases.
• Practice Worksheet Pack - You will find five practice worksheets here.
• Write the Equation Worksheet Pack - We give you the words. We want the integers in return.
• Two Step Equations in Words Lesson Practice Sheet - This one was written well. I think I'm on version 30 of this.
• Two Step Equations in Words Worksheet - Now you not only need to write the equation, but solve it too.
• Answer Keys - These are for all the unlocked materials above.

Homework Sheets

Start by getting x by itself. The next step is to take a sentence and turn into a math sentence that is then solvable.

• Homework 1 - In order to get x on the left side we have to remove 4 using addition.
• Homework 2 - Write the sentence as an equation and solve it. Four less than a number divided by 3 is six.
• Homework 3 - For the first step, in order to get x on the left side we have to remove 12 using subtraction.

Practice Worksheets

The sentence based problems really give many students trouble.

• Practice 1 - It is always good to start with numbers that have no variables attached to them.
• Practice 2 - In the second step we will remove the coefficient using division. The opposite of multiplication is division.
• Practice 3 - Write the sentences as equations and solve.

Math Skill Quizzes

Remind students to combine like terms as much as possible and then proceed from there.

• Quiz 1 - Write the sentences as equations and solve. You are basically trying to represent what is presented with numbers and symbols.
• Quiz 2 - Solve for p: 6p + 2p = 72. There are some single steps in here too to allow for some confidence.
• Quiz 3 - You will find you deal a lot with negative values here. Just remember to counter the operations.

How to Approach Two-Step Equations

When you start to learn algebra, it gets more complicated every step of the way. Nonetheless, after learning a single-step equation in which you only have to switch numbers to the other side of the relational operator. For instance, when you have an equation like x + 3 = 0, you need to subtract 3 (since it's the same number on the left-hand-side) on both sides to have an equation x + 3 - 3 = 0 - 3. The answer will be x = -3. However, to solve the two-step equation, we have to learn one more single step. Let's learn it in the form of an example.

For example, we will take the equation 3x + 5 = 65. The entire goal is to get the variable (x) by itself.

The first step, in this case, will be to subtract 5 from both sides of the relational sign (3x + 5 – 5) = (65 – 5).

The result is 3x = 60; however, you haven't found the value of x alone. There is a coefficient attached to x.

In such circumstances, you need to divide with the same number as the coefficient attached to the variable. Therefore, we will divide both sides with 3. 3x / 3 = 60 / 3. So x = 20.

It is all about determining what operations are in play and then just drop the opposites to cancel them out, as you have seen in our example.

The Two Steps You Need to Solve These Problems

These problems can seem much more reasonable when you put them into perspective and think in this manner when tackling them:

1) Start by countering the math operations that are presented to you. Just remember that addition and subtraction will counter one another. Multiplication and division are adversaries as well. Whatever operation you choose to use to create balance, just use the same operation on both sides of the equation and you are all set. This will help you tip the scales in your favor.

2) The last step is just to get the variable by itself. This will again require you to counter the operations that are in place, and you are good to go.

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Home > Math Worksheets > Algebra Worksheets > Two Step Equations

Two step math equations are algebraic problems that require you to make two moves to find the value of the unknown variable. For example, using the equation 3x + 5 = 11 we will need to perform two steps to find the value of x. The first step would be to get the constant values of the equation by themselves. In this case 5 and 11 are our constants. We can always perform any operation to the equation as long as we perform the same operation to both sides of the equation. If we want to get the 5 and 11 together, we can perform the opposite operation that is already taking place with one of them. If we were to subtract 5 from both sides, we would be left with 3x = 6. That is step one. For step two we need to get rid of the 3 that is next to the variable. To undo multiplication, we can divide. If we were to divide both sides by 3, we would be left with x = 2. When we start out with algebraic equations, most teacher prefer to name the unknown variable x and stay consistent with its use. Equations of lines often are most frequently solved in two steps.

In this section, your students will work on solving for two variables in algebraic expressions and graphing the results. This set of worksheets introduces your students to the concept of solving for two variables, and provides examples, short practice sets, longer sets of questions, and quizzes. In everyday math, in the real world, a survey of daily tasks of over 1,200 was issued by UMASS. They found that two-step math problems were the most common mathematical tasks people were performing. Utilize these worksheets to demonstrate how to solve two step problems. Students will learn how to create equations from number sentences and solve them.

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Print two step equations worksheets, click the buttons to print each worksheet and associated answer key., solving two step equation problems worksheet 1.

Solve for x in the following 12 problems. Example: 2x + 4 = 12

Worksheet 2

Remember to flip the symbol of the constant that has an operation first. Example: 7x + 4 = 46

Two Step Problems Worksheet 1 (contains negatives)

Do not let the negative value throw you off the scent of the answer. Example: - 4x + 4 = - 12

Worksheet 2 (contains negatives)

You can reorder the problem before you start working on it. Example: - 3 + 7x = 4

Worksheet 3 (contains negatives)

Solve for x in the following 12 problems. Example: 3x + 4 = - 8

More Basic Worksheet 4

The arrange of values is the key here. Example: 5 - 3x = 8

Worksheet 5

See how fast you can complete all of these problems. Example: 3x + 4 = 19

Worksheet 6

See if you can start with the variable first. It is a good way to make sure you master this. Example: 3 + 2x = 17

Two Step Problems Worksheet 7

Solve for x in the following 12 problems. Example: 7 + 2x = 19

Worksheet 8

More practice to make sure you know what you are doing. Example: 6x + 1 = 13

Decimals- Meet the Skill

Learn how to solve the problem: x/2 + 3.5 = 21 Check by substituting your solution to the equation.

Try the Skill

Write an equation and solve for this number sentence: "When a number is divided by 5 and the result added to 35, the result is 105."

Practice the Skill

Solve the equations. Check by substituting your solution to the equation. Example: 9 = a/4+ 4

Practice the Skill Twice

Write an equation and solve for the following 10 sentences.

Show the Skill

These turn up the heat and are more difficult. Example: -13 = -5x + 7

Setup Equations Warm Up

Write an equation and solve for the following 3 sentences.

Meet the Skill

Define the variable, write the equation and solve it: "Three more than two times a number is forty-three."

Where is the variable? Create an equation and solve it: "Two less than a number divided by 5 is eight."

For the following 10 problems locate the unknown variable and make an equation. Oh yeah, solve it too! Example: "Seven less than a number divided by 3 is five."

What final value is being described by the math sentences? Example: "Two more than a number divided by 3 is eleven."

This problems are great to help you start thinking algebraically.

Why not read the problem and take an educated guess before you break down the algebra?

Writing Two-Step Equations - Lesson

We show you how to complete all the following problems.

Practice Worksheet 1

You don't always need to use the variable x. Try using something more abstract to make it interesting.

It is always a good idea to write the components of the equation in the same order as the sentence.

Review Sheet

This walks you through all the steps you need to know.

Practice this skill by completing the 6 problems on this sheet.

See how well you know this topic.

"Do Now"

This is designed to be used as a whole class activity.

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Unit 6 – Linear Equations and Inequalities

Solutions to Equations

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

SMART NOTEBOOK

Two-Step Equations

More Work with Two-Step Equations

Manipulating Expressions within Equations

Recognizing Structure to Solve Two-Step Equations

Solving Word Problems with Two-Step Equations Day 1

Solving Word Problems with Two-Step Equations Day 2

Solving Two-Step Inequalities

An Interesting Property of Inequalities

Modeling with Inequalities

Unit Review

Unit 6 Review

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit 6 Assessment Form A

EDITABLE ASSESSMENT

Unit 6 Assessment – Form B

Unit 6 Exit Tickets

Unit 6 Mid-Unit Quiz – Form A

Unit 6 Mid-Unit Quiz – Form B

U06.AO.01 – Practice Solving Two Step Equations

EDITABLE RESOURCE

U06.AO.02 – Practice with Modeling with Two-Step Equations

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• Grade 8 McGraw Hill Glencoe - Answer Keys

Explanation:

\(16 = 5\text{x} - 9\)

\(3 - 8\text{c} = 35\)

\(-\cfrac{1}{2}\text{x} - 7 = -11\)

\(15 - \cfrac{\text{w}}{4} = 28\)

\(-3 - 6\text{x} = 9\)

Larina received a $50 gift card to an online store. She wants to purchase some bracelets that cost $8 each. There will be a $10 overnight delivery fee. Solve \(8\text{n} + 10 = 50\) to find the number of bracelets she can purchase.

LaTasha paid $75 to join a summer golf program. The course where she plays charges $30 per round. Since she is a student, she receives a $10 discount per round. If LaTasha spent $375, use the equation \(375 = 20\text{g} + 75\) to find how many rounds of golf LaTasha played.

Copy and Solve Solve each equation. Show your work in a separate piece of paper.

\(\cfrac{\text{a} - 4}{5} = 12\)

\(\cfrac{\text{n} + 3}{8} = -4\)

\(\cfrac{6 + \text{z}}{10} = -2\)

Reason Abstractly If Mr. Arenth wants to put new carpeting in the room shown, how many square feet should he order?

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Unit 1: Algebra foundations

Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.

Solving Two-Step Equations Cut and Paste Activity w/ Answer Key

Description

Designed to be a confidence builder for students just learning how to solve two-step equations or for students struggling to master the skill. Can be used in class or for homework. Answer key provided as a time-saver for easy grading.

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