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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.

1. 4x + 2x – 3 = 9

Fill in the blank(s):

 Equations that contain like terms must be simplified ___________they can

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

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

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.

3. 3(a + 12) = 1 – 2(a – 5)  Problem Set: Solving Multiple-Step Equations – Part 2

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  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, > Fill in the blank(s):

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

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.

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.

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 