Finding Equivalent Expression and Solutions

A rectangle has a length of (5 + 2x) inches and a width of 10 inches. A triangle has a base of 30 inches and a height of (4x - 10) inches. The area in square inches of the rectangle is equal to the area in square inches of the triangle. What is the value of x?

• 2.5

• 3

• 7.5

• 5

What is the solution to the equation 5(2w + 4) = 4(2w + 9)?

• w = 5/2

• w = 8

• w = 28/9

• w = 5

What is the solution to 4(q + 56.5) = 30q – 112?

Record your answer in the box

Mathematical Equivalence

ON

What is the solution to this equation? 2(40 - 5y) = 10y + 5(1 - y)

• A) 7.5

• B) 15

• C) 5

• D) Not here

What is the solution to this equation? -4(2m - 7) = 3(52 - 4m)

• 32

• 46

• -6.4

• -40.75

Which value of x makes the equation 1.25(4x – 10) = 7.5 true?

x=​ (a)  

• 3.5
• -1
• -0.5
• 4

What value of n makes the equation 4(0.5n – 3) = n – 0.25(12 – 8n) true?

Mathematical Equivalence

ON

What value of x makes the equation -5x - (-7 - 4x) = -2(3x - 4) true?

What is the solution set for -4x + 10 ≥ 5x + 55?

• x ≥ 5

• x ≥ 45

• x ≤ –5

• x ≤ –45

Which inequality describes all the solutions to 5(3 - x) < -2x + 6?

• x < -9

• x > 3

• x < -3

• x > 7