Efficiently Solving Inequalities

When solving an inequality, what is the main things that are different from solving equations.

• Draw the line

• Use inverse operations to solve.

• Bring down the inequality symbol and FLIP the symbol  when you multiply or divide by a negative.

Solve for k. 

7k – 2 ≥ -9

• k ≤ -1

• k≤1

• k≥1

• k ≥ -1

Solve for k.
2k - 9≤ -19

• k ≤ -5

• k ≤ 5

• k < -5

• k < 5

Solve the inequality.
x + 5 ≤ 13

• x ≥ 8

• x ≥ 18

• x ≤ 8 

• x ≤ 18 

Solve the inequality 5x - 8 ≤ 27.

• x ≥ 7

• x = 27

• x ≤ 7

• x ≤ 5

What would be the first step in solving the inequality for 2x+7>15?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide both sides by 2

• Multiply both sides by 2

To solve the inequality:

x/3 < 4

What needs to be done first?

• Multiply both sides by 3.

• Divide both sides by 3.

• Add 3 to both sides.

• Subtract 3 from both sides.

3x - 2 ≥ 34

• x ≥ -12

• x ≤ -12

• x ≤ 12

• x ≥ 12