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QuestionSolve the equation: 1−2x−15=3−6−4x51-\frac{2 x-1}{5}=3-\frac{6-4 x}{5}.

Studdy Solution

STEP 1

Assumptions1. The equation is 1−x−15=3−6−4x51-\frac{ x-1}{5}=3-\frac{6-4 x}{5}

STEP 2

First, we will simplify the equation by multiplying each term by5 to eliminate the fractions.
5×(1−2x−15)=5×(−6−4x5)5 \times \left(1-\frac{2 x-1}{5}\right) =5 \times \left(-\frac{6-4 x}{5}\right)

STEP 3

istribute the5 into each term on both sides of the equation.
5−(2x−1)=15−(6−x)5 - (2x -1) =15 - (6 -x)

STEP 4

implify the equation by removing the parentheses.
−2x+1=15−6+4x -2x +1 =15 -6 +4x

STEP 5

Combine like terms on both sides of the equation.
−2x=9+4x -2x =9 +4x

STEP 6

To isolate the variable x, we will move the term -2x from the left side to the right side by adding2x to both sides of the equation.
6=9+4x+2x6 =9 +4x +2x

STEP 7

implify the right side of the equation by combining like terms.
6=9+6x6 =9 +6x

STEP 8

To isolate the variable x, we will move the constant from the right side to the left side by subtracting from both sides of the equation.
6−=6x6 - =6x

STEP 9

implify the left side of the equation.
−3=6x-3 =6x

STEP 10

Finally, to solve for x, we will divide both sides of the equation by6.
x=−36x = \frac{-3}{6}

STEP 11

implify the right side of the equation to find the value of x.
x=−0.5x = -0.5So, the solution to the equation is x=−0.5x = -0.5.

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