Question

Please help me solve each question! Make sure to show work so I can earn full credit.

1. 5x – 5 ≥ 10 or -3x + 1 > 13

2. 5x + 3 ≤ 18 and 4 - x < 6

Answer 1

(1)

`5x-5\geq10\,\,\mbox{or}\,\,-3x+1>13\\5x\geq15\,\,\mbox{or}\,\,-3x>12\\x\geq3\,\,\mbox{or}\,\,x<-4\\-\infty<x<-4\,\,\mbox{or}\,\,3\leq x<\infty`

(2)

`5x + 3\leq18 \,\,\mbox{and}\,\,4 - x < 6\\5x\leq15 \,\,\mbox{and}\,\,- x < 2\\x\leq3 \,\,\mbox{and}\,\,x > 2\\2<x\leq 3\\x\in(2,3]`

Answer 2

1. x < -4 or x ≥ 3

2. -2 < x ≤ 3

Explanation:

1. 5x - 5 ≥ 10

5x ≥ 15

x ≥ 3

-3x + 1 > 13

-3x > 12

x < -4

Solution is x < -4 or x ≥ 3

2. 5x + 3 ≤ 18

5x ≤ 15

x ≤ 3

4 - x < 6

-x < 2

x > - 2

answer is -2 < x ≤ 3