1. What is the solution to the system of linear equations?

1.

2x – 5y = 14     multiply through by 6  →  12x - 30y   = 84     (1)

7x + 6y = -2      multiply through by 5 →   35x + 30y  = -10    (2)

Add  (1)  and (2)

47x  = 74

x = 74 / 47

And using  2x  - 5y  = 14     we have

2(74/47) - 5y  = 14

148 / 47  - 5y  = 14

148/47  - 14   = 5y

148 /47  - 658 / 47  =  5y

-510 / 147  = 5y    divide both sides by 5

-102 / 147  = y

2. Heather is 6 years younger than 5 times her daughter's age. The sum of their ages is greater than 90.

What is the youngest age Heather's daughter can be?

Let her daughter's age  =  D

Heather's age  is 5D - 6

And we have that

D + 5D - 6 > 90    simplify

6D - 6 > 90     add 6 to both sides

6D  > 96       divide both sides by 6

D > 16

Her daughter  must  be at least 17

3. What is the interval notation for the compound inequality?

-5 > a or a > 4

a < - 5   or   a  > 4

( -infinity, -5) or (4, infinity )

4. Plot the inequality on the number line

x < -2 or x > 5

5. Solve for x.

-14 < 3x -  2x < 7

-14 < x < 7

In interval notation

(-14, 7)

6. Solve for x.

-14 < 3x + 5 or 1/2x + 5 > 7

-14 < 3x     divide both sides by 3

-14/3 < x

(1/2)x +  5 > 7     multiply through by 2

x + 10  > 14    subtract 10 from both sides

x >   4

So

x > - 14/3   or   x > 4

We must choose the  most restrictive interval that solves both equations

This  is    x > 4