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

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

2x – 5y = 14

7x + 6y = -2

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?

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

-5 > a or a > 4

4. Plot the inequality on the number line

x < -2 or x > 5

5. Solve for x.

-14 < 3x - 2 x < 7

6. Solve for x.

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

thank you for the help

Aug 22, 2018

#1
+100529
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1.

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

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

Aug 22, 2018
#2
+100529
+2

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

Aug 22, 2018
#3
+100529
+2

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 )

Aug 22, 2018
edited by CPhill  Aug 22, 2018
#4
+100529
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4. Plot the inequality on the number line

x < -2 or x > 5

Aug 22, 2018
#5
+100529
+2

5. Solve for x.

-14 < 3x -  2x < 7

-14 < x < 7

In interval notation

(-14, 7)

Aug 22, 2018
#6
+100529
+2

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

Aug 22, 2018