Solving and Graphing Inequalities Worksheet

Question 1

Solve the inequality: x + 7 < 15.

Accepted Answer

The solution is x < 8 because subtracting 7 from both sides gives x < 8.

Question 2

Solve the inequality: y - 4 ≥ 10.

Accepted Answer

The solution is y ≥ 14 because adding 4 to both sides gives y ≥ 14.

Question 3

Solve the inequality: 3a ≤ 21.

Accepted Answer

The solution is a ≤ 7 because dividing both sides by 3 gives a ≤ 7.

Question 4

Solve the inequality: n/5 > 6.

Accepted Answer

The solution is n > 30 because multiplying both sides by 5 gives n > 30.

Question 5

Solve the inequality: -2m < 12.

Accepted Answer

The solution is m > -6 because dividing both sides by -2 reverses the inequality symbol.

Question 6

Solve the inequality: -4p ≥ 20.

Accepted Answer

The solution is p ≤ -5 because dividing both sides by -4 reverses the inequality symbol.

Question 7

Solve the inequality: 2x + 5 < 17.

Accepted Answer

The solution is x < 6. Subtract 5 from both sides to get 2x < 12, then divide both sides by 2.

Question 8

Solve the inequality: 5k - 8 ≥ 27.

Accepted Answer

The solution is k ≥ 7. Add 8 to both sides to get 5k ≥ 35, then divide both sides by 5.

Question 9

Solve the inequality: (r/3) + 2 ≤ 9.

Accepted Answer

The solution is r ≤ 21. Subtract 2 from both sides to get r/3 ≤ 7, then multiply both sides by 3.

Question 10

Solve the inequality: 18 - 3t > 6.

Accepted Answer

The solution is t < 4. Subtract 18 from both sides to get -3t > -12, then divide by -3 and reverse the inequality symbol.

Question 11

Graph the solution x > 2 on a number line. Describe the circle and the direction of shading.

Accepted Answer

The graph has an open circle at 2 and shading to the right because x can be any number greater than 2, but not 2 itself.

Question 12

Graph the solution y ≤ -1 on a number line. Describe the circle and the direction of shading.

Accepted Answer

The graph has a closed circle at -1 and shading to the left because y can be -1 or any number less than -1.

Question 13

Write an inequality for the graph described: closed circle at 4 with shading to the left.

Accepted Answer

The inequality is x ≤ 4 because the closed circle includes 4 and the shading left represents values less than 4.

Question 14

Write an inequality for the graph described: open circle at -3 with shading to the right.

Accepted Answer

The inequality is x > -3 because the open circle does not include -3 and the shading right represents values greater than -3.

Question 15

A movie theater charges a $6 entry fee plus $3 per snack. Maya has at most $21 to spend. Write and solve an inequality to find how many snacks, s, she can buy.

Accepted Answer

The inequality is 6 + 3s ≤ 21. Subtracting 6 gives 3s ≤ 15, and dividing by 3 gives s ≤ 5, so Maya can buy at most 5 snacks.

Solving and Graphing Inequalities

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