Study Guide Equations and Expressions

A bakery has made 20 cakes this week. They plan to bake the same number of cakes each day for the rest of the week. There are 5 days left in the week. The bakery needs to bake at least 45 cakes to meet its goal. Write an inequality that represents this situation, where c is the number of cakes baked each day.

•  5c+20≤45

•  5c−20≥45

• 45≤20+5c

• 45≥20+5c

Select all expressions that are equivalent to −3(y−2)+5y−6.

•  2y

•  −3y+6+5y−6

•  −3y−6+5y−6

• 2y−12

Which number line shows all the values of x that make the inequality 4x−5≤15 true?

• x≤5, solid circle at 5, shading to the left.

• x≥5, open circle at 5, shading to the right.

• x≤5, open circle at 5, shading to the left.

• x≥5, solid circle at 5, shading to the right.

At the start of a dive, a diver was at an elevation of 10 feet above sea level. The diver descends at a rate of 5 feet per minute. Write an inequality that represents t, the number of minutes after the start of the dive, when the diver's elevation was lower than -20 feet below sea level.

• 10−5t<−20

• 10−5t>−20

• 10<−20-5t

• 10>−20-5t

A swimmer has completed 12 laps in the pool. She plans to swim the same number of laps each day for the rest of the week. There are 4 days left in the week. She wants to swim at least 28 laps by the end of the week. Write an inequality that represents this situation, where l is the number of laps she swims each day.

• 4l+12≥28

• 4l−12≤28

• 28≥12+4l

• 28≤12+4l

Which number line shows all the values of y that satisfy the inequality 2y+3>9?

• y>3, open circle at 3, shading to the right.

• y≤3, solid circle at 3, shading to the left.

• y≥3, solid circle at 3, shading to the right.

• y<3, open circle at 3, shading to the left.

Select all expressions that are equivalent to −2(d−5)+3d−10.

• d

•  −2d+10+3d−10

• −2d−10+3d−10
  

• d−20

Factor to write an equivalent expression: −8c+12d

• −4(2c−3d)

• 4(-2c+3d)

• −4(-8c+12d)

• 3(-4c+4d)