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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Multiple-Step Equations

Solving Multiple-Step Equations (Part 1) – Variable on One Side

Instructions:

Follow along with video and fill in the blanks as indicated. Space has been provided for
you to show all work on this sheet and take any additional notes.

Example: Copy steps/answers from video.

1. 4x + 2x – 3 = 9

Fill in the blank(s):

 Equations that contain like terms must be simplified ___________they can

Examples: Copy steps/answers from video.

2. 7m – m + 5 = 14

3. 12y + 3y – 8y = –12 + 33

4. 4(a + 3) + 6a = –4

5. 14 – (6x + 2) + 8x = –14 + 20

Notes: __________________________________________________________________________
________________________________________________________________________________

Problem Set: Solving Multiple-Step Equations – Part 1

Solve and check your solutions.

1. 4m – 6m + 8m = –20 – 4

2. –3x – 4 – 8x + 6 = –20

3. –6 + 8 = 4y + 3(y + 5) – 6

4. –6 + 8 = 4y – 3(y + 5) – 6

5. 2(m – 3) – 4(m + 6) = 18

Lesson 8 (cont’d): Solving Multiple-Step Equations (Part 2) – Variable on Both Sides

Examples: Copy steps/answers from video.

1. 3x – 2 = 6x + 7

2. 4(x – 3) + 8 = 2x – 2 + 12

Fill in the blank(s):

 Steps for Solving Linear Equations 1. Remove any _______________________and combine like terms on each side of the equation. 2. Use the Addition Property of Equality to get: a. the __________________ terms on ____________ and/or b. the __________________ terms on the other side. 3. Use the Multiplication/Division Property of Equality to get the __________________ of the variable term equal to a “1”. 4. ____________your answer.

Copy steps/answers from video.

3. 3(a + 12) = 1 – 2(a – 5)

Problem Set: Solving Multiple-Step Equations – Part 2

Solve and check your solutions.

1. –5m + 3 = 2m – 4

2. –4x – 2(x + 5) – 3x = 13 + 8 + x

3. 3y + 2(y – 4) = 12 y + 5

4. 8m – (m + 2) + 4 = 4m – 7

Lesson 8 (cont’d): Strategies – Decimals and Fractions

Examples: Copy steps/answers from video.

3. 0.3 – 0.5(x + 3) = 1.4 – 0.6x

4. 0.4(2x + 5) = 2.3 – (x + 3)

Notes: _________________________________________________________________________

Problem Set: Solving Equations with Decimals and Fractions

Solve by first clearing the fractions and decimals. Check at least two solutions.

3. 2.1x + 6.5 = 4.1 – 3.9x

Solve without clearing the fractions or decimals.

4. 0.6 – 2(a – 1) = 0.2 + 5 – a

Lesson 8 (cont’d): Solving Inequalities

Fill in the blank(s):

 An __________________ is two expressions separated by one of the following symbols: Less than, < Less than or equal, < Greater than, > Greater than or equal, >

Examples: Copy steps/answers from video.

Fill in the blank(s):

 Addition Property for Inequalities Given an inequality, we can ______ the same number to _______ sides of the inequality.

Copy steps/answers from video.

3. y + 6 < 12

4. x – 3 > 12

5. 12 < – 4 + x

Consider the following inequality: Copy steps/answers from video.

2 < 3

2 < 3

Fill in the blank(s):

 Multiplication/Division Property for Inequalities Given an inequality, you can multiply or divide ________sides by the same non-zero number. Note: _______________ the inequality symbol when multiplying or dividing by a _______________number.

Copy steps/answers from video.

7. –2x + 4 < 8

8. 2x + 4 < 8

Fill in the blank(s):

 Steps for Solving Inequalities 1. __________________ each side by removing parentheses and combining like terms, as needed. 2. Use the Addition Rule, if needed, to _____________ the _____________ term on one side. 3. Use the Multiplication/Division Rule to make the ________________ a ____________. Note: ___________________the inequality symbol when multiplying or dividing by a _______________ number.

Copy steps/answers from video.

9. 6x – 8x + 12 < 3x – 12

10. 3(x – 2) – 8x + 9 > –16 + 5

Problem Set: Solving Inequalities

Solve and check your solutions. Draw a number line graph of your solution.

2. –8p + 5 > 21

3. 3m – 8m + 7 < 18 – 5

4. –2(x + 4) + 3x < 2x – 5