Math

QuestionSolve the equation: 2x53+17=3x9\frac{2 x-5}{3}+\frac{1}{7}=3 x-9.

Studdy Solution

STEP 1

Assumptions1. The equation given is x53+17=3x9\frac{ x-5}{3}+\frac{1}{7}=3 x-9 . We are asked to solve the equation for xx

STEP 2

First, we need to eliminate the fractions in the equation. We can do this by multiplying every term by the least common multiple (LCM) of the denominators, which in this case is21.
212x5+2117=21(x9)21 \cdot \frac{2 x-5}{} +21 \cdot \frac{1}{7} =21 \cdot ( x-9)

STEP 3

Now, simplify the equation.
14(2x5)+3=63x18914 (2 x-5) +3 =63 x -189

STEP 4

Expand the terms.
28x70+3=63x18928 x -70 +3 =63 x -189

STEP 5

Combine like terms.
28x67=63x18928 x -67 =63 x -189

STEP 6

To isolate xx, we can subtract 28x28x from both sides of the equation.
67=35x189-67 =35 x -189

STEP 7

Next, add 189189 to both sides of the equation.
122=35x122 =35 x

STEP 8

Finally, divide both sides by 3535 to solve for xx.
x=12235x = \frac{122}{35}So, the solution to the equation is x=12235x = \frac{122}{35}.

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