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6-8 Accelerated 7 Unit 4 Lesson 8

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 •Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 4, Lesson 8

Solving Any Linear Equation

Accelerated 7

Practice

Problem 1

Solve each of these equations. Explain or show your reasoning.

\(2(x+5)=3x+1\)

\(3y-4=6-2y\)

\(3(n+2)=9(6-n)\)

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Lesson 8 Resources

Student Materials

Problem 2

Clare solves an equation, but when she checks her answer she notices that her solution is incorrect. She knows she made a error, but she can’t find it. Help Clare find the error and correctly solve the equation.

\(\begin{align} 12(5+2y)&=4y-(5-9y)\\ 72+24y&=4y-5-9y\\ 72+24y&=\text-5y-5\\ 24y&=\text-5y-77\\ 29y&=\text-77\\ y&=\frac {\text{-}77}{29}\ \end{align}\)

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Problem 3

Solve each equation and check your solution.

\(\frac19(2m-16) = \frac13(2m+4)\)

\(\text-4(r+2)=4(2-2r)\)

\(12(5+2y)=4y-(6-9y)\)

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Problem 4

Kiran wrote the expression \(x-10\) to represent this number puzzle: “Pick a number, add -2, and multiply by 5.”

Lin thinks Kiran made a mistake.

How can she convince Kiran he made a mistake?
What would be a correct expression for this number puzzle?

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Problem 5

ForLesson 5: Keeping the Equation Balanced

Label the arrows to describe each move.

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Problem 6

ForLesson 13: Solutions of Inequalities

Represent the solution for each inequality on the number line.

\(x>7\)
\(x\geq\text-4.2\)

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