1. Solving Two-Step Inequalities
COURSE 3 LESSON 2-8
Solve –5x – 2 > –12.
–5x – 2 > –12
–5x – > – Add 2 to each side.
–5x > –10 Simplify.
Divide each side by –5. Reverse the direction of the inequality.
–10 –5
–5x
<
x < 2 Simplify.
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2. Solving Two-Step Inequalities
COURSE 3 LESSON 2-8
(continued)
Check
Step 1 See if 2 is a solution to the related equation.
–5x – 2 = –12 Write the related equation.
–12 = –12
–5(2) – 2 = –12 Substitute 2 for x.
–10 – 2 = –12 Use the order of operations.
Step 2 Check the inequality symbol. Choose any number less than 2 and substitute it into the original inequality. In this case, try 0.
–5x – 2 > –12
–5(0) – 2 > –12 Substitute 0 for x.
–2 > –12
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3. Solving Two-Step Inequalities
COURSE 3 LESSON 2-8
You have $50 to spend on CDs that cost $7 each and one CD player that costs $29. How many CDs can you buy?
cost of one
CD player
< –
Words plus cost of CDs is at most $50
Let c = the number of CDs.
Inequality • c 50
• c 50
< –
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4. Solving Two-Step Inequalities
COURSE 3 LESSON 2-8
(continued)
29 – • c – 29 Subtract 29 from each side.
< –
7c Simplify.
< –
Divide each side by 7.
< – 7c 7 21
c Simplify.
You can buy 3 CDs.
Check for Reasonableness Each CD costs $7. The cost of the CD player plus three CDs would be $7(3) + $29, or $50, the amount you have to spend. You would spend $50 or less if you bought the CD player and 3 or fewer CDs.
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5. Solving Two-Step Inequalities
COURSE 3 LESSON 2-8
Solve.
1. 3x – 11 > –2
3. You want to order one large photo of yourself for $8.95
and some small photos for your friends. The small photos
cost $.75 each. You have $25 to spend. Write an inequality
you can use to find how many small photos you can order.
Then solve it. r –4
> –
x > 7 r
< –
0.75p ; p ; 21 or fewer small photos
< –
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