Inequalities on the ACT

Which of the following is equivalent to the inequality -8 + 6p ≤ 4 - 3p?

• p ≤ 1/3

• p ≤ 4/3

• p ≥ 3/4

• p ≥ 3

• p ≤ 12

Given numbers r and q, where 0 < r < q, which of the following inequalities must be true for all values of r and q?

• r + 2 > q + 2

• r/q > 1

• 1/q > 1/r

• r³ > q ³

• -r > -q

At a grocery store, muffins sell for $4.00 per package, and cookies sell for $6.25 per package. These bakery items are only sold in packages. Dwayne wants to buy at least one package of muffins and one package of cookies for a party, and he must spend exactly $58.00. What is the maximum number of packages of cookies that he can buy?

• 4

• 5

• 7

• 8

• 9

The inequality -3x/5 + 2 > 8 is equivalent to which of the following inequalities?

• x < -18/5

• x < -10/3

• x < -10

• x > -10

• x > 10

To win the school art competition, the finalists must receive over 50% of the votes cast by their peers. If 330 students vote and x represents the minimum number of votes a finalist needs to win the competition, which of the following expressions is true?

• x < 165

• x = 165

• x > 165

• x < 166

• x > 166

The real number line graph is represented by which of the following inequalities?

• -3 ≤ x ≤ 3

• -3 ≤ x < 4

• 0 ≤ x < 4

• 3 ≤ x ≤ 4

• 4 < x ≤ -3

The number line graph is represented by which of the following inequalities?

• -2 ≤ x and 5 ≤ x

• -2 ≤ x and 5 ≥ x

• -2 ≤ x or 5 ≤ x

• -2 ≥ x or 5 ≥ x

• -2 ≥ x or 5 ≤ x

The solution set for the inequality 2x - 7 ≥ 3 is represented by which of the graphs?

• A

• B

• C

• D

• E

Which of the following is a possible value for y if [ 3y -3 ] = 6 ?

• -2

• -1

• 0

• 1

What is the smallest positive integer y such that [3 - y] > 6 ?

• 2

• 6

• 7

• 9

• 10