solve inequality

Question

Solve the inequality. Then graph your solution.

1) x+3<1
2) x-2≥-1
3) 3x>9
4) -x-5≥-4
5) -x+2<-3

Answer 1

1)x+.3 < 1

Apply subtraction property of inequality: Subtract 3 from each side.

x+3-3 < 1-3

x < -2

2) x-2 ≥ -1

Apply addition property of inequality: Add 2 to each side.

x-2+2 ≥ -1+2

x ≥ 1

3) 3x > 9

Apply division propeerty of inequality: Divide each side by 3.

3x/3 > 9/3

x > 3

4) -x-5 ≥ -4

Apply addition property of inequality: Add 5 to each side.

-x+5-5 ≥ -4+5

-x ≥ 1

Multiply each side by negative one and flip the symbol.

-(-x) ≤  -1

x ≤ -1

5) -x+2 < -3

Apply subtraction property of inequality: Subtract 2 from each side.

-x+2-2 < -3-2

-x < -5

Multiply each side by negative one and flip the symbol.

 

-(-x) > -(-5)

x > 5