Solving MultiStep Inequalities

1
Solving Multi-Step Inequalities
2
Solve

• 3x 8 lt -10
• Subtract 8 from both sides.
• 3x 8 8 lt -10 8
• 3x lt -18
• Divide by 3
• x lt- 6

• Add six to both sides

• Multiply both sides by 2

3
Solve

• 3(2x 4) lt 2(4x 4)
• Distribute
• 6x 12 lt 8x 8
• Subtract 8x from both sides
• 6x 12 - 8x lt 8x 8 8x
• -2x 12 lt -8

• Add 12 to both sides.
• -2x 12 12 lt -8 12
• -2x lt 4
• Divide both sides by 2. Because you divided by
  a negative number, you must flip the inequality
  symbol.
• x gt -2

4
Solve

• The perimeter of a rectangle is no more than 26
  cm. The width is 6 cm. Write an inequality for
  all the possible lengths of this rectangle.
• 2L 2w P
• 2L 2(6) lt 26
• 2L 12 lt 26

5

• 2L 12 lt 26
• 2L 12 12 lt 26 12
• 2L lt 14
• 2L/2 lt 14/2
• L lt 7 cm

6
Try these

• The perimeter of a rectangle is at least 45 cm.
  The length is 15 cm. Write an inequality for all
  possible widths of this rectangle.
• -3(x 8) gt -2(5x 9)

7
Try theseanswers

• The perimeter of a rectangle is at least 45 cm.
  The length is 15 cm. Write an inequality for all
  possible widths of this rectangle.
  W gt 7.5 cm
• -3(x 8) gt -2(5x 9) x gt 6
• x gt -44
• x gt 79