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Answer:
x=9
Step-by-step explanation:
Solve for x
(
x
+
2
3
x
)
−
1
3
(
x
+
2
3
x
)
=
10
Simplify
x
+
2
3
x
−
1
3
⋅
(
x
+
2
3
x
)
.
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Simplify each term.
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x
+
2
x
3
−
5
x
9
=
10
Find the common denominator.
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x
⋅
9
9
+
2
x
⋅
3
9
−
5
x
9
=
10
Combine fractions with similar denominators.
x
⋅
9
+
2
x
⋅
3
−
5
x
9
=
10
Subtract
5
x
from
x
⋅
9
.
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2
x
⋅
3
+
4
⋅
x
9
=
10
Multiply
3
by
2
.
6
x
+
4
⋅
x
9
=
10
Add
6
x
and
4
⋅
x
.
10
x
9
=
10
Multiply both sides of the equation by
9
10
.
9
10
⋅
10
x
9
=
9
10
⋅
10
Simplify both sides of the equation.
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Simplify
9
10
⋅
10
x
9
.
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x
=
9
10
⋅
10
Cancel the common factor of
10
.
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Cancel the common factor.
x
=
9
10
⋅
10
Rewrite the expression.
x
=
9
Answer:
x = 9
Step-by-step explanation:
Given
(x + [tex]\frac{2}{3}[/tex] x ) - [tex]\frac{1}{3}[/tex](x + [tex]\frac{2}{3}[/tex] x ) = 10 ← distribute parenthesis
x + [tex]\frac{2}{3}[/tex] x - [tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{9}[/tex] x = 10
Multiply through by 9 ( the LCM of 3 and 9 ) to clear the fractions
9x + 6x - 3x - 2x = 90
10x = 90 ( divide both sides by 10 )
x = 9