Solving and Graphing Inequalities
Use inverse operations and number lines to represent solution sets
Solving and Graphing Inequalities
Use inverse operations and number lines to represent solution sets
Math - Grade 6-8
- 1
Solve the inequality: x + 7 < 15.
Undo the addition by subtracting 7 from both sides.
The solution is x < 8 because subtracting 7 from both sides gives x < 8. - 2
Solve the inequality: y - 4 ≥ 10.
The solution is y ≥ 14 because adding 4 to both sides gives y ≥ 14. - 3
Solve the inequality: 3a ≤ 21.
Divide both sides by the positive number 3.
The solution is a ≤ 7 because dividing both sides by 3 gives a ≤ 7. - 4
Solve the inequality: n/5 > 6.
The solution is n > 30 because multiplying both sides by 5 gives n > 30. - 5
Solve the inequality: -2m < 12.
When you divide by a negative number, flip the inequality symbol.
The solution is m > -6 because dividing both sides by -2 reverses the inequality symbol. - 6
Solve the inequality: -4p ≥ 20.
The solution is p ≤ -5 because dividing both sides by -4 reverses the inequality symbol. - 7
Solve the inequality: 2x + 5 < 17.
Use inverse operations in reverse order: subtract first, then divide.
The solution is x < 6. Subtract 5 from both sides to get 2x < 12, then divide both sides by 2. - 8
Solve the inequality: 5k - 8 ≥ 27.
The solution is k ≥ 7. Add 8 to both sides to get 5k ≥ 35, then divide both sides by 5. - 9
Solve the inequality: (r/3) + 2 ≤ 9.
First isolate r/3, then undo the division by 3.
The solution is r ≤ 21. Subtract 2 from both sides to get r/3 ≤ 7, then multiply both sides by 3. - 10
Solve the inequality: 18 - 3t > 6.
The solution is t < 4. Subtract 18 from both sides to get -3t > -12, then divide by -3 and reverse the inequality symbol. - 11
Graph the solution x > 2 on a number line. Describe the circle and the direction of shading.
A greater than symbol points to values larger than the boundary number.
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. - 12
Graph the solution y ≤ -1 on a number line. Describe the circle and the direction of shading.
The graph has a closed circle at -1 and shading to the left because y can be -1 or any number less than -1. - 13
Write an inequality for the graph described: closed circle at 4 with shading to the left.
Closed circles match ≤ or ≥.
The inequality is x ≤ 4 because the closed circle includes 4 and the shading left represents values less than 4. - 14
Write an inequality for the graph described: open circle at -3 with shading to the right.
The inequality is x > -3 because the open circle does not include -3 and the shading right represents values greater than -3. - 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.
At most means less than or equal to the total amount.
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.