Linear Inequalities

Solve the Inequality

100

x+5<12

x<7

200

3x>15

x>5

300

2x−7≤9

x≤8

400

5−2x>1

x<2

500

3(x−4)≤2x+5

x≤17

Sign Flip

100

−2x>6

x<−3

200

−x/3≤4

x≥−12

300

−4x+5>13

x<−2

400

−2(x−3)≤8

x≥−1

500

(−3x+6)/(-2)>4

x>14/3

Find the Mistake

100

x+3<10

x<7
Final answer: x>7

Final inequality sign is reversed incorrectly

200

−2x>8
x>−4

Forgot to flip the inequality sign

300

3x−6≤9 

3x≤3 

x≤1

Computation error: x≤5

400

−x+4<1 

−x<−3 

x<3

Did not flip inequality after multiplying by −1

500

x+1>2x+5 

-4>x

the minimum integer value of x is -3

x=-3 is max. integer value

Logic and Understanding

100

True or False:
If x>3, then 2x>6

True

200

Which is greater:
All solutions of x<−2 OR all solutions of x>−2?

x>-2

300

True or False:
Multiplying both sides of an inequality by a negative number keeps the sign the same.

False, it flips the sign

400

If x≤5, is x=5 a solution? Explain briefly.

Yes

500

Which inequality represents:
“All numbers between 2 and 6, including 2 but not 6”?

2≤x<6

Different Problems

100

Solve: 4x+3<2x+11

x<4

200

Solve: 3(2x−1)≥5x+4

x≥7

300

Solve the compound inequality:
2<x+1≤7

1<x≤6

400

Solve:
(x-2)/3+4>6

x>8

500

Create your own inequality that has the solution:
x>3
(Any valid inequality is acceptable)

Example: x−1>2 (answers may vary)