Linear Inequalities Worksheets Page 19
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50Example 5
Empty Set and All Reals
Solve each inequality. Check your solution.
a. 9t - 5(t - 5) ≤ 4(t - 3)
9t - 5(t - 5) ≤ 4(t - 3)
Original inequality
9t - 5t + 25 ≤ 4t - 12
Distributive Property
4t + 25 ≤ 4t - 12
Combine like terms.
4t + 25
- 4t
≤ 4t - 12
- 4t
Subtract 4t from each side.
Study
Tip
25 ≤ -12
Simplify.
Empty Set
Set-builder
Since the inequality results in a false statement, the solution set is the empty
notation is not required when
set, ∅.
the solution set is the empty
set. Instead, the solution is
b. 3(4m + 6) ≤ 42 + 6(2m - 4)
written as the symbol ∅.
3(4m + 6) ≤ 42 + 6(2m - 4)
Original inequality
12m + 18 ≤ 42 + 12m - 24
Distributive Property
12m + 18 ≤ 12m + 18
Combine like terms.
12m + 18
- 12m
≤ 12m + 18
- 12m
Subtract 12m from each side.
18 ≤ 18
Simplify.
All values of m make the inequality true. All real numbers are solutions.
GuidedPractice
Solve each inequality. Check your solution.
5A. 18 - 3(8c + 4) ≥ -6(4c - 1)
5B. 46 ≤ 8m - 4(2m + 5)
Check Your Understanding
= Step-by-Step Solutions begin on page R12.
Example 1
1.
CANOEING
If four people plan to use the canoe with 60 pounds of
supplies, write and solve an inequality to find the allowable
average weight per person.
2.
SHOPPING
Rita is ordering a movie for $11.95 and a few CDs. She has $50 to spend. Shipping
and sales tax will be $10. If each CD costs $9.99, write and solve an inequality to find the
greatest number of CDs that she can buy.
Example 2
Solve each inequality. Graph the solution on a number line.
_
2
6h - 10 ≥ 32
4. -3 ≤
r + 9
3
3
5. -3x + 7 > 43
6. 4m - 17 < 6m + 25
Example 3
Define a variable, write an inequality, and solve each problem. Then check your
solution.
7. Four times a number minus 6 is greater than eight plus two times the number.
8. Negative three times a number plus 4 is less than five times the number plus 8.
Examples 4–5
Solve each inequality. Graph the solution on a number line.
9. -6 ≤ 3(5v - 2)
10. -5(g + 4) > 3(g - 4)
11. 3 - 8x ≥ 9 + 2(1 - 4x)
298
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Lesson 5-3
Solving Multi-Step Inequalities
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