Chapter 12 Section 4
Solving Multi-Step Inequalities
Example 1
Solve 9 + 3x < 27. Check your solution.
9 + 3x < 27
9 - 9 + 3x < 27 - 9
3x < 18
3 3
x<6
Check
Substitute 6 and a number less than 6 into the
inequality.
Let x = 0
Let x = 6
9 + 3(0) < 27
9 + 3(6) < 27
9 < 27
9 + 18 < 27
True
27 < 27
False,
The solution is {x l x < 6}.
Your Turn
Solve each inequality. Check your solution.
4 + 2x ≤ 12
{x l x ≤ 4}
Your Turn
Solve each inequality. Check your solution.
8x - 5 ≥ 11
{x l x ≥ 2}
Solving inequalities is similar to solving
equations. The only exception is that with
inequalities, you must reverse the inequality
symbol if you multiply or divide by a negitive
number.
Example 3
Solve -4x + 3 ≥ 23 + 6x. Check your solution.
-4x + 3 ≥ 23 + 6x
-4x – 6x + 3 ≥ 23 + 6x – 6x
-10x + 3 ≥ 23
-10x + 3 - 3 ≥ 23 – 3
-10x ≥ 20
-10 -10
Reverse the
symbol
x ≤ -2
Your solution is {x l x ≤ -2}. Check your solution.
Your Turn
Solve each inequality. Check your solution.
10 – 5x < 25
{x l x > -3}
Your Turn
Solve each inequality. Check your solution.
3x + 1 > -17
{x l x < 6}
Example 4
Solve 8 ≤ -2(x – 5). Check your solution.
8 ≤ -2(x – 5)
8 ≤ -2x + 10
8 - 10 ≤ -2x + 10 – 10
-2 ≤ -2x
Reverse the
symbol
-2 -2
1≥x
The solution is {x l x ≤ 1). Check your solution.
Your Turn
Solve each inequality. Check your solution.
2 > -(x + 7)
{x l x > -9}
Your Turn
Solve each inequality. Check your solution.
3(x – 4) ≤ x - 5
{x l x ≤ 3.5}
Hannah’s scores on the first three of four 100
point tests were 85, 92, and 90. What score
must she receive on the fourth test to have a
mean score of more than 92 for all tests?
Explore
Let s = Hannah’s score on the fourth test.
The sum of Hannah’s four test scores, divided by
4, will give the mean score. The mean must
be more than 92.
Plan
The sum of Hannah’s four test scores, divided by
4, will give the mean score. The mean must
be more than 92.
Solve
85 + 92+ 95+ s > 92
4
4 (85 + 92+ 95+ s ) > 4(92)
4
85 + 92+ 95+ s > 368
267 - 267 + s > 368 - 267
s > 101
Examine
Substitute a number greater than 101, such as
102, into the original problem. Hannah’s
average would be 92.25. Since 92.25 > 92 is a
true statement, the solution is correct.
Hannah’s must score more than 101 points
out of a 100 point test. Without extra credit,
this is not possible. So, Hannah cannot have a
mean over 92.