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QuestionSolve the equation 3x−15−29x=12453x - \frac{1}{5} - \frac{2}{9}x = \frac{124}{5}. Combine like terms and isolate xx.

Studdy Solution

STEP 1

Assumptions1. The given equation is 3x−15−9x=12453x - \frac{1}{5} - \frac{}{9}x = \frac{124}{5} . The goal is to isolate the variable xx on one side of the equation

STEP 2

First, we need to combine like terms on the left side of the equation. The like terms are xx and −29x-\frac{2}{9}x.
x−29x=279x−29xx - \frac{2}{9}x = \frac{27}{9}x - \frac{2}{9}x

STEP 3

Now, subtract the fractions on the left side of the equation.
279x−29x=259x\frac{27}{9}x - \frac{2}{9}x = \frac{25}{9}xSo, the simplified equation becomes259x−15=1245\frac{25}{9}x - \frac{1}{5} = \frac{124}{5}

STEP 4

Next, isolate the variable term by adding 1\frac{1}{} to both sides of the equation.
259x−1+1=124+1\frac{25}{9}x - \frac{1}{} + \frac{1}{} = \frac{124}{} + \frac{1}{}

STEP 5

implify the equation.
259x=1255\frac{25}{9}x = \frac{125}{5}

STEP 6

To solve for xx, divide both sides of the equation by 259\frac{25}{9}.
x=1255×925x = \frac{125}{5} \times \frac{9}{25}

STEP 7

implify the equation to find the value of xx.
x=5×91=45x =5 \times \frac{9}{1} =45So, the solution to the equation is x=45x =45.

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