Question

2/3x - 11 = x/3 + 3

Answer 1

2
3

−
1
1
=

3
+
3
2
3
x
−
11
=
x
3
+
3
32​x−11=3x​+3
2

3
−
1
1
=

3
+
3
2
x
3
−
11
=
x
3
+
3
32x​−11=3x​+3
2
Find common denominator
2

3
−
1
1
=

3
+
3
2
x
3
−
11
=
x
3
+
3
32x​−11=3x​+3
2

3
+
3
(
−
1
1
)
3
=

3
+
3
2
x
3
+
3
(
−
11
)
3
=
x
3
+
3
32x​+33(−11)​=3x​+3
3
Combine fractions with common denominator
2

3
+
3
(
−
1
1
)
3
=

3
+
3
2
x
3
+
3
(
−
11
)
3
=
x
3
+
3
32x​+33(−11)​=3x​+3
2

+
3
(
−
1
1
)
3
=

3
+
3
2
x
+
3
(
−
11
)
3
=
x
3
+
3
32x+3(−11)​=3x​+3
4
Multiply the numbers
2

+
3
(
−
1
1
)
3
=

3
+
3
2
x
+
3
(
−
11
)
3
=
x
3
+
3
32x+3(−11)​=3x​+3
2

−
3
3
3
=

3
+
3
2
x
−
33
3
=
x
3
+
3
32x−33​=3x​+3
5
Find common denominator
2

−
3
3
3
=

3
+
3
2
x
−
33
3
=
x
3
+
3
32x−33​=3x​+3
2

−
3
3
3
=

3
+
3
⋅
3
3
2
x
−
33
3
=
x
3
+
3
⋅
3
3
32x−33​=3x​+33⋅3​
6
Combine fractions with common denominator
2

−
3
3
3
=

3
+
3
⋅
3
3
2
x
−
33
3
=
x
3
+
3
⋅
3
3
32x−33​=3x​+33⋅3​
2

−
3
3
3
=

+
3
⋅
3
3
2
x
−
33
3
=
x
+
3
⋅
3
3
32x−33​=3x+3⋅3​
7
Multiply the numbers
2

−
3
3
3
=

+
3
⋅
3
3
2
x
−
33
3
=
x
+
3
⋅
3
3
32x−33​=3x+3⋅3​
2

−
3
3
3
=

+
9
3
2
x
−
33
3
=
x
+
9
3
32x−33​=3x+9​
8
Multiply all terms by the same value to eliminate fraction denominators
2

−
3
3
3
=

+
9
3
2
x
−
33
3
=
x
+
9
3
32x−33​=3x+9​
3
⋅
2

−
3
3
3
=
3
(

+
9
3
)
3
⋅
2
x
−
33
3
=
3
(
x
+
9
3
)
3⋅32x−33​=3(3x+9​)
9
Cancel multiplied terms that are in the denominator
3
⋅
2

−
3
3
3
=
3
(

+
9
3
)
3
⋅
2
x
−
33
3
=
3
(
x
+
9
3
)
3⋅32x−33​=3(3x+9​)
2

−
3
3
=

+
9
2
x
−
33
=
x
+
9
2x−33=x+9
10
Add
3
3
33
33
to both sides of the equation
2

−
3
3
=

+
9
2
x
−
33
=
x
+
9
2x−33=x+9
2

−
3
3
+
3
3
=

+
9
+
3
3
2
x
−
33
+
33
=
x
+
9
+
33
2x−33+33=x+9+33
11
Simplify
Add the numbers
Add the numbers
2

=

+
4
2
2
x
=
x
+
42
2x=x+42
12
Subtract

x
x
from both sides of the equation
2

=

+
4
2
2
x
=
x
+
42
2x=x+42
2

−

=

+
4
2
−

2
x
−
x
=
x
+
42
−
x
2x−x=x+42−x
13
Simplify
Combine like terms
Multiply by 1
Combine like terms

=
4
2
x