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QuestionSolve for xx in the equation: 2x+4−32x=13(x+5)2x + 4 - \frac{3}{2}x = \frac{1}{3}(x + 5).

Studdy Solution

STEP 1

Assumptions1. The equation is in the form x+4−3x=13(x+5)x +4 - \frac{3}{}x = \frac{1}{3}(x +5). We are solving for xx

STEP 2

First, we need to clear the fraction on the left side of the equation. To do this, we can multiply every term in the equation by2.
2⋅2x+2⋅4−2⋅2x=2⋅1(x+5)2 \cdot2x +2 \cdot4 -2 \cdot \frac{}{2}x =2 \cdot \frac{1}{}(x +5)

STEP 3

implify the equation.
x+8−3x=23(x+5)x +8 -3x = \frac{2}{3}(x +5)

STEP 4

Next, we need to clear the fraction on the right side of the equation. To do this, we can multiply every term in the equation by3.
3⋅(4x+8−3x)=3⋅23(x+)3 \cdot (4x +8 -3x) =3 \cdot \frac{2}{3}(x +)

STEP 5

implify the equation.
12x+24−9x=2(x+5)12x +24 -9x =2(x +5)

STEP 6

Expand the right side of the equation.
12x+24−9x=2x+1012x +24 -9x =2x +10

STEP 7

Combine like terms on the left side of the equation.
3x+24=2x+103x +24 =2x +10

STEP 8

To isolate xx, subtract 2x2x from both sides of the equation.
3x−2x+24=2x−2x+103x -2x +24 =2x -2x +10

STEP 9

implify the equation.
x+24=x +24 =

STEP 10

Finally, to solve for xx, subtract24 from both sides of the equation.
x+24−24=10−24x +24 -24 =10 -24

STEP 11

implify the equation to find the solution for xx.
x=−14x = -14So, the solution to the equation is x=−14x = -14.

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