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6-8 Accelerated 7 Unit 4 Lesson 5

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

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Unit 4, Lesson 5

Keeping the Equation Balanced

Accelerated 7

Practice

Problem 1

Which of the changes keeps the hanger in balance?

Select all that apply.

<p>Balanced hanger. Left side, 1 triangle and 1 square. Right side, 2 circles and 1 triangle.</p><br>

Adding two circles on the left and a square on the right
Adding two triangles to each side
Adding two circles on the right and a square on the left
Adding a circle on the left and a square on the right
Adding a triangle on the left and a square on the right

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Lesson 5 Resources

Student Materials

Problem 2

Here is a balanced hanger diagram.

Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and \(x\) represents the weight of each square. Select all equations that represent a balanced hanger.

<p>A balanced hanger. Left side, 4 squares, 2 triangles, 2 circles. Right side, 2 squares, 1 triangle, 3 circles.</p><br>

\(x+x+x+x+11=x+11.5\)
\(2x=0.5\)
\(4x+5+6=2x+2.5+6\)
\(2x+2.5=3\)
\(4x+2.5+2.5+3+3=2x+2.5+3+3+3\)

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Problem 3

What is the weight of a square if a triangle weighs 4 grams?

Explain your reasoning.

<p>Balanced hanger. Left side, 1 triangle, 2 squares. Right side, 3 triangles, 1 square. </p><br>

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Problem 4

ForLesson 4: Combining Like Terms (Part 2)

In each row, decide whether the expression in column A is equivalent to the expression in column B. If they are not equivalent, show how to change one expression to make them equivalent.

A

\(3x-2x+0.5x\)
\(3(x+4) - 2(x+4)\)
\(6(x+4)-2(x+5)\)
\(3(x+4) - 2(x+4) +0.5(x+4)\)
\(20\left(\frac25x + \frac34y - \frac12\right)\)

B

\(1.5x\)
\(x+3\)
\(2(2x+7)\)
\(1.5\)
\(\frac12(16x + 30y - 20)\)

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Problem 5

ForLesson 13: Solutions of Inequalities

A sign on the road says, “Speed limit: 60 miles per hour.”

Let \(s\) be the speed of a car. Write an inequality that matches the information on the sign.
Draw a number line to represent the solutions to the inequality.
Could 60 be a value of \(s\)? Explain your reasoning.

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