Math Journal 10-14
Solve for x.
1.
1
− 𝑥
3
+ 10 = 6
2. 2𝑥 + 8 − 6𝑥 = 3𝑥 − 6
Solve the inequality for x, make a number line and graph the solution.
3. 𝑥 − 13 ≤ −14
4.
1
− 𝑥
4
−2>6
Unit 3 Day 6: Solving MultiStep Inequalities
Essential Question: How do I solve inequalities
that require more than two steps?
Process/Steps
SIMPLIFY:
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.
-3
x-3>
-9
5
+3
+3
-3 x > -6 · 5
5·
5
-3x > -30
-3
-3
x < 10
To get rid of a fraction:
1) Multiply by the denominator
2) 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
5x - 8 > 2
+ 8 +8
4x< 32
5x > 10
4 4
x< 8
5
5
x>2
Example 3: Solve the inequality. Check your solutions.
2x – 9x + 17 > -4
4x – 9 + 3x < 5
-7x + 17 > -4
- 17 - 17
7x - 9 < 5
+9 +9
-7x > -21
7x < 14
-7
-7
x<3
7
7
x<2
Example 4: Solve the inequality.
5x + 3(x + 4) > 28
5x+ 3x+ 12> 28
8x+ 12> 28
-12 - 12
8x > 16
8
8
x >2
4x – 3(x – 2) < 21
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
2x - 5x + 45> 27
16x- 36 < 28
-3x + 45> 27
+36 +36
- 45 -45
16x < 64
-3x > - 18
16
-3
16
x <4
x<6
-3
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.