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QuestionSolve 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 given equation is x+4−3x=13(x+5)x +4 - \frac{3}{}x = \frac{1}{3}(x +5). We need to solve for xx

STEP 2

First, simplify the left side of the equation. Combine like terms.
2x−2x+4=1(x+5)2x - \frac{}{2}x +4 = \frac{1}{}(x +5)

STEP 3

To simplify the expression, convert the whole numbers to fractions with denominator2.
2x−32x+=13(x+5)\frac{}{2}x - \frac{3}{2}x + = \frac{1}{3}(x +5)

STEP 4

Subtract the fractions on the left side of the equation.
42x−32x=12x\frac{4}{2}x - \frac{3}{2}x = \frac{1}{2}xSo, the equation becomes12x+4=13(x+)\frac{1}{2}x +4 = \frac{1}{3}(x +)

STEP 5

Next, distribute the 13\frac{1}{3} on the right side of the equation.
12x+4=13x+53\frac{1}{2}x +4 = \frac{1}{3}x + \frac{5}{3}

STEP 6

To make the equation easier to work with, multiply every term by6 to eliminate the fractions.
6⋅12x+6⋅4=6⋅13x+6⋅536 \cdot \frac{1}{2}x +6 \cdot4 =6 \cdot \frac{1}{3}x +6 \cdot \frac{5}{3}

STEP 7

implify each term.
3x+24=2x+103x +24 =2x +10

STEP 8

Subtract 2x2x from both sides of the equation to get the xx terms on one side.
3x−2x+24=2x−2x+103x -2x +24 =2x -2x +10

STEP 9

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

STEP 10

Subtract24 from both sides of the equation to solve for xx.
x+24−24=10−24x +24 -24 =10 -24

STEP 11

implify the equation to get the solution.
x=10−24=−14x =10 -24 = -14So, the solution to the equation is x=−14x = -14.

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