Question

Please help give working please

Answer 1

1. a = -6

4 = 2(a + 8)

Divide both sides by 2.

`(4)/(2)` = a + 8

Divide 4 by 2 to get 2.

2 = a + 8

Swap sides so that all variable terms are on the left-hand side.

a + 8 = 2

Subtract 8 from both sides.

a = 2 - 8

Subtract 8 from 2 to get −6.

a = -6

2. y = -3

−4(3+y)=12(−3−y)

Use the distributive property to multiply −4 by 3+y.

−12−4y=12(−3−y)

Use the distributive property to multiply 12 by −3−y.

−12−4y=−36−12y

Add 12y to both sides.

−12−4y+12y=−36

Combine −4y and 12y to get 8y.

−12+8y=−36

Add 12 to both sides.

8y=−36+12

Add −36 and 12 to get −24.

8y=−24

Divide both sides by 8.

y =
`(-24)/(8)`

Divide −24 by 8 to get −3.

y = -3

3. c = 2

−6+7c=2(c+2)

Use the distributive property to multiply 2 by c+2.

−6+7c=2c+4

Subtract 2c from both sides.

−6+7c−2c=4

Combine 7c and −2c to get 5c.

−6+5c=4

Add 6 to both sides.

5c=4+6

Add 4 and 6 to get 10.

5c=10

Divide both sides by 5.

c =
`(10)/(5)`

Divide 10 by 5 to get 2.

c = 2

4. a = 1

−(a−9)=8a

To find the opposite of a−9, find the opposite of each term.

−a−(−9)=8a

The opposite of −9 is 9.

−a+9=8a

Subtract 8a from both sides.

−a+9−8a=0

Combine −a and −8a to get −9a.

−9a+9=0

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

−9a=−9

Divide both sides by −9.

a =
`(-9)/(-9)`

Divide −9 by −9 to get 1.

a = 1

5. x = 27

7x=−3(−2x−9)

Use the distributive property to multiply −3 by −2x−9.

7x=6x+27

Subtract 6x from both sides.

7x−6x=27

Combine 7x and −6x to get x.

x=27

6. p = 9

2(3p−7)=40

Divide both sides by 2.

3p−7=
`(40)/(2)`

Divide 40 by 2 to get 20.

3p−7=20

Add 7 to both sides.

3p=20+7

Add 20 and 7 to get 27.

3p=27

Divide both sides by 3.

p=
`(27)/(3)`

Divide 27 by 3 to get 9.

p=9

7. a = -8

4a+77−5(1−a)=0

Use the distributive property to multiply −5 by 1−a.

4a+77−5+5a=0

Subtract 5 from 77 to get 72.

4a+72+5a=0

Combine 4a and 5a to get 9a.

9a+72=0

Subtract 72 from both sides. Anything subtracted from zero gives its negation.

9a=−72

Divide both sides by 9.

a=
`(-72)/(9)`

Divide −72 by 9 to get −8.

a=−8

8. x = -1

2(x−7)=−2(x+9)

Use the distributive property to multiply 2 by x−7.

2x−14=−2(x+9)

Use the distributive property to multiply −2 by x+9.

2x−14=−2x−18

Add 2x to both sides.

2x−14+2x=−18

Combine 2x and 2x to get 4x.

4x−14=−18

Add 14 to both sides.

4x=−18+14

Add −18 and 14 to get −4.

4x=−4

Divide both sides by 4.

x=
`(-4)/(4)`

Divide −4 by 4 to get −1.

x=−1

Hope it helps and have a great day!

=D ~sunshine~