What is the answer to each equation?

2x+4(−2x+3)=
6
3(2x+2)

+4

2
Distribute
2
x
−
8
x
+
12
=
3
(
2
x
+
2
)
6
+
4
2x−8x+12=
6
3(2x+2)

+4

3
Combine like terms
−
6
x
+
12
=
3
(
2
x
+
2
)
6
+
4
−6x+12=
6
3(2x+2)

+4

4
Simplify fraction
−
6
x
+
12
=
2
x
+
2
2
+
4
−6x+12=
2
2x+2

+4

5
Find common denominator
−
6
x
+
12
=
2
x
+
2
2
+
2
⋅
4
2
−6x+12=
2
2x+2

+
2
2⋅4


6
Combine fractions with common denominator
−
6
x
+
12
=
2
x
+
2
+
2
⋅
4
2
−6x+12=
2
2x+2+2⋅4


7
Multiply the numbers
−
6
x
+
12
=
2
x
+
2
+
8
2
−6x+12=
2
2x+2+8


8
Add the numbers
−
6
x
+
12
=
2
x
+
10
2
−6x+12=
2
2x+10


9
Subtract
12
12 from both sides of the equation
−
6
x
+
12
−
12
=
2
x
+
10
2
−
12
−6x+12−12=
2
2x+10

−12

10
Simplify
−
6
x
=
2
x
−
14
2
−6x=
2
2x−14


11
Eliminate fraction denominators
2
(
−
6
)
x
=
2
⋅
2
x
−
14
2
2(−6)x=2⋅
2
2x−14


12
Cancel multiplied terms that are in the denominator
2
(
−
6
)
x
=
2
x
−
14
2(−6)x=2x−14

13
Multiply the numbers
−
12
x
=
2
x
−
14
−12x=2x−14

14
Subtract
2
x
2x from both sides of the equation
−
12
x
−
2
x
=
2
x
−
14
−
2
x
−12x−2x=2x−14−2x

15
Simplify
−
14
x
=
−
14
−14x=−14

16
Divide both sides of the equation by the same factor
−
14
x
−
14
=
−
14
−
14
−14
−14x

=
−14
−14


17
Simplify
x
=
1
x=1

SOLUTION

x
=
1
x=1