Math Journal 10-14Solve for x.
1. 2.
Solve the inequality for x, make a number line and graph the solu-tion.
3. 4.
Unit 3 Day 6: Solving Multi-Step Inequalities
Essential Question: How do I solve inequalities that require more than two
steps?
Process/StepsSIMPLIFY:
1) Apply the distributive property, if necessary
2) Combine like terms on each side
Isolate the variable and SOLVE by:
3) Drawing a line under the inequality sign
4) Undo addition or subtraction
5) Undo multiplication or division. If you used a negative number, FLIP THE INEQUALITY SIGN!!
ALWAYS:
6) Plug in and check your solution!
Example 1: Solve the inequality.
x - 3 > -9 -35
+ 3 + 3
-35
x > -6 · 5 5 ·
-3x > -30
-3 -3
x < 10
To get rid of a fraction:
1) Multiply by the denominator2) Divide by the numerator
OR
Multiply by the reciprocal
Example 2: Solve the inequality. Check your solutions.
7x – 3x – 8 < 24 4x – 8 + x > 2
4x - 8< 24+ 8 + 8
4x< 32
4 4x< 8
5x - 8> 2+ 8 +8
5x> 10
5 5x> 2
Example 3: Solve the inequality. Check your solutions.
2x – 9x + 17 > -4 4x – 9 + 3x < 5
-7x+ 17> -4
- 17 - 17
-7x> -21
-7 -7
x< 3
7x - 9< 5
+ 9 + 9
7x< 14
7 7
x< 2
Example 4: Solve the inequality.
5x + 3(x + 4) > 28 4x – 3(x – 2) < 21
5x+ 3x+ 12> 28
8x+ 12> 28-12 - 12
8x> 16
8 8
x > 2
4x- 3x+ 6< 21
x + 6< 21-6 - 6
x< 15
Example 5: Solve the inequality.
4x + 12(x - 3) < 28 2x – 5(x – 9) > 27
4x+ 12x- 36< 28
16x- 36 < 28
+36 +36
16x< 64
2x- 5x+ 45> 27
-3x+ 45> 27
- 45 -45
-3x> - 18
16 16
x< 4
-3 -3
x< 6
Summary
Essential Questions: How do I solve inequalities that require more than two steps?
Take 1 minute to write 2 sentences answering the essential questions.
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