9 3 Solving MultiStep Inequalities Math 9 We

9. 3 Solving Multi-Step Inequalities Math 9

We can solve inequalities using the exact same methods learned in Chapter 8. Our goal is to ISOLATE the variable. ***REMEMBER to not forget how the inequality signs work when doing algebra steps!!! Recall some steps used to ISOLATE the variable:

Adding a positive number to both Multiply a positive number to sides… no change to the sign both sides… no change to the sign Subtract a positive number from Divide both sides by a positive both sides… no change to the sign number … no change to the sign Adding a negative number to both Multiply a negative number to sides… no change to the sign both sides… FLIP the sign Subtract a negative number from Divide both sides by a negative both sides… no change to the sign number … FLIP the sign

• Solve each inequality and interpret the solution using a number line.

1. 4 x + 11 > 35 -11 4 x >24 ÷ 4 X > 6 3 4 5 6 7 8 9

• 2. 0 10 20 30 40 50 60

3. 5 - 2 x > 10 x + 29 +2 x 5 > 12 x +29 -29 -24 > 12 x ÷ 12 -2 > x -5 -4 -3 -2 -1 0 1

4. 4( x -2) ≤ 5 x -12 Distribute the 4 into the brackets 4 x -8 ≤ 5 x - 12 -4 x -8 ≤ x -12 +12 4 ≤ x 0 1 2 3 4 5 6

Example 5 – Solving Problems Using Inequalities Danny has his own computer repair business. He offers his customers two payment options. Option A has a base fee of $40 plus $8 per hour. Option B has no base fee but costs $15 per hour. How many hours does a repair job have to take in order for option B to be less expensive? a) Model this problem using an inequality. Let h = hours on the job 40 + 8 h > 15 h b) After how many hours will option B be less expensive?

b) After how many hours will option B be less expensive? 40 + 8 h > 15 h -8 h 40 > 7 h ÷ 7 5. 7 > h Therefore jobs shorter than 5. 7 hours will be less expensive with option B.

Time for 9. 3 Warm-up