Lesson 14

Strategic Solving

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Problem 1

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

\(2b+8-5b+3=\text-13+8b-5\)

\(2x+7-5x+8=3(5+6x)-12x\)

\(2c-3=2(6-c)+7c\)

Solution

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Problem 2

Solve each equation and check your solution.

\(\text-3w-4=w+3\)

\(3(3-3x)=2(x+3)-30\)

\(\frac13(z+4)-6=\frac23(5-z)\)

Solution

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Problem 3

Elena said the equation \(9x+15=3x+15\) has no solutions because \(9x\) is greater than \(3x\). Do you agree with Elena? Explain your reasoning.

Solution

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Problem 4

Which of the changes would keep the hanger in balance?

Select all that apply.

Balanced hanger. Left side, 1 triangle and 1 square. Right side, 2 circles and 1 triangle.

 

A:

Adding two circles on the left and a square on the right

B:

Adding 2 triangles to each side

C:

Adding two circles on the right and a square on the left

D:

Adding a circle on the left and a square on the right

E:

Adding a triangle on the left and a square on the right

Solution

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(From Unit 4, Lesson 12.)