MAC Inequalities

1 Step

100

3x ≥ 21

x ≥ 7

200

12x < 48

x < 4

300

-13x < 65

x > -5

400

-18x ≥ 54

x ≤ - 3

500

6x > -90

x > -15

Sign stays the same, you didn't DIVIDE by a negative number!!! Gotcha. 

2 Step

100

3x + 5 < 21

x < 5

200

4x - 7 ≤ 41

x ≤ 12

300

-3x -4 > 14

x < - 6

400

-4x + 8 ≥ 48

x ≤ -10 

500

6x + 6 > -30

x > -6

You didn't DIVIDE by a negative so the sign stays the same! Gotcha. 

X's on both sides

100

2x > 16 - 2x 

x > 4

200

3x - 12 ≤ 9x 

x ≤ -2

300

5x + 24 > 13x 

x > 3

400

-3x - 36 > -9x 

x < 6

You DID divide by a negative, sign flips! 

500

7x - 63 ≥ 10x 

x ≥ -21

Extreme

100

-4(x + 2) < 68

x > -19

200

6 + 3(x - 9) ≤ 3

x ≤ 8

300

-3(x - 4) > 2(x + 5) 

2/5 > x     OR    x < 2/5 

Depends on how you solve it. 

400

9 + 3 + 2x - 12 + 5x > 14

x > 2

500

7 + 8(x - 2) ≥ 9 - 2(x + 5) +10 

x ≥ 1 4/5     OR     1 4/5 ≤ x

Distribute

100

2(x + 2) ≥ 18

x ≥ 7

200

3(x - 3) < -30

x < -7

300

-4(x + 2) ≤ 40

x ≥ -12

400

4(x + 3) > -2(x + 3) 

x > 3   OR  -3 < x

It depends on how you solve it, but both are correct answers. 

500

-7(x + 2) < 9x -4

-5/9 < x     OR     x > -5/9

Depends on how you solve it.