8a - (15 - a) = 6 (a - 7) + 15

Question

Mathematics

Brynlee Sherman

29 May, 14:55

8a - (15 - a) = 6 (a - 7) + 15

+5

Answers (2)

Know the Answer?

Davin Harris · Answer 1

Davin Harris 29 May, 15:30

0

The correct answer is a=-4

Karlee Villanueva · Answer 2

a = - 4 or 3a+12=0 (not sure what you want)

Step-by-step explanation:

Solve for a:

8 a - (15 - a) = 6 (a - 7) + 15

- (15 - a) = a - 15:

8 a + a - 15 = 6 (a - 7) + 15

Grouping like terms, 8 a + a - 15 = (8 a + a) - 15:

(8 a + a) - 15 = 6 (a - 7) + 15

8 a + a = 9 a:

9 a - 15 = 6 (a - 7) + 15

6 (a - 7) = 6 a - 42:

9 a - 15 = 6 a - 42 + 15

Grouping like terms, 6 a - 42 + 15 = 6 a + (15 - 42):

9 a - 15 = 6 a + (15 - 42)

15 - 42 = - 27:

9 a - 15 = 6 a + - 27

Subtract 6 a from both sides:

(9 a - 6 a) - 15 = (6 a - 6 a) - 27

9 a - 6 a = 3 a:

3 a - 15 = (6 a - 6 a) - 27

6 a - 6 a = 0:

3 a - 15 = - 27

Add 15 to both sides:

3 a + (15 - 15) = 15 - 27

15 - 15 = 0:

3 a = 15 - 27

15 - 27 = - 12:

3 a = - 12

Divide both sides of 3 a = - 12 by 3:

(3 a) / 3 = (-12) / 3

3/3 = 1:

a = (-12) / 3

The gcd of - 12 and 3 is 3, so (-12) / 3 = (3 (-4)) / (3*1) = 3/3*-4 = - 4:

Answer: |

| a = - 4Solve for a:

8 a - (15 - a) = 6 (a - 7) + 15

- (15 - a) = a - 15:

8 a + a - 15 = 6 (a - 7) + 15

Grouping like terms, 8 a + a - 15 = (8 a + a) - 15:

(8 a + a) - 15 = 6 (a - 7) + 15

8 a + a = 9 a:

9 a - 15 = 6 (a - 7) + 15

6 (a - 7) = 6 a - 42:

9 a - 15 = 6 a - 42 + 15

Grouping like terms, 6 a - 42 + 15 = 6 a + (15 - 42):

9 a - 15 = 6 a + (15 - 42)

15 - 42 = - 27:

9 a - 15 = 6 a + - 27

Subtract 6 a from both sides:

(9 a - 6 a) - 15 = (6 a - 6 a) - 27

9 a - 6 a = 3 a:

3 a - 15 = (6 a - 6 a) - 27

6 a - 6 a = 0:

3 a - 15 = - 27

Add 15 to both sides:

3 a + (15 - 15) = 15 - 27

15 - 15 = 0:

3 a = 15 - 27

15 - 27 = - 12:

3 a = - 12

Divide both sides of 3 a = - 12 by 3:

(3 a) / 3 = (-12) / 3

3/3 = 1:

a = (-12) / 3

The gcd of - 12 and 3 is 3, so (-12) / 3 = (3 (-4)) / (3*1) = 3/3*-4 = - 4:

Answer: a = - 4