Ordering and Equations Review

What value of k makes this equation true?

• k = -2
• k = -8
• k = 8/3
• k = 2

What value of x makes this model true?

• -4

• -2

• -1

• 3

What value of x makes the following equation true?

5x - 14 = 8x + 4

• x = 6

• x = -6

• x = -18/13

• x = 10/3

Answer explanation

To solve the equation 2x + 3 = x - 4, first subtract x from both sides to get x + 3 = -4. Then, subtract 3 from both sides to isolate x, resulting in x = -7. Therefore, the correct choice is -7.

Which of the following real numbers is least?

• 7.1

• $6\pi$
  

• $\frac{20}{3}$
  

• $\sqrt{51}$
  

The diagonal lengths of three rectangles are shown. The rectangles are not drawn to scale.

Which list shows the rectangles in order by their diagonal lengths from shortest to longest?

• Rectangle T, Rectangle S, Rectangle P

• Rectangle T, Rectangle P, Rectangle S

• Rectangle S, Rectangle T, Rectangle P

• Rectangle S, Rectangle P, Rectangle T

Which best represents point Z on the number line?

• √165

• √149

• √12.2

• √13

Which is the best approximation of point P?

• √8

• √2.8

• 17/5

• 2 1/4

Julie started with 20 pieces of gum and gave away x pieces. Conrad started with 35 pieces of gum and gave away twice as many pieces as Julie did.

How many pieces of gum did Julie give away if they had the same number of pieces of gum left?

• 18

• 5

• 15

• 8

Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.

Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallon per minute.

After how many minutes will both aquariums contain the same amount of water?

• 148 min

• 125 min

• 25 min

• 50 min