Studdy AI Logo
Math

QuestionSolve the equation: 3−3−2x4=1−x8−13 - \frac{3 - 2x}{4} = \frac{1 - x}{8} - 1

Studdy Solution

STEP 1

Assumptions1. We are given the equation 3−3−x4=1−x8−13-\frac{3- x}{4}=\frac{1-x}{8}-1 . We are asked to find the value of xx that satisfies this equation

STEP 2

First, we need to simplify the equation. We can do this by multiplying each term by the least common multiple (LCM) of the denominators to eliminate the fractions. The LCM of4 and8 is8.
8×(−−2x4)=8×(1−x8−1)8 \times \left(-\frac{-2 x}{4}\right) =8 \times \left(\frac{1-x}{8}-1\right)

STEP 3

istribute the8 to each term in the equation.
24−2(3−2x)=1−x−824-2(3-2 x) =1-x-8

STEP 4

implify each side of the equation.
24−6+4x=1−x−824-6+4x =1-x-8

STEP 5

Combine like terms on each side of the equation.
18+4x=−x−718+4x = -x-7

STEP 6

Add xx to both sides of the equation to bring all terms involving xx to one side.
18+4x+x=−18+4x+x = -

STEP 7

implify the left side of the equation.
18+5x=−718+5x = -7

STEP 8

Subtract18 from both sides of the equation to isolate the term with xx.
5x=−7−185x = -7-18

STEP 9

implify the right side of the equation.
5x=−255x = -25

STEP 10

Finally, divide both sides of the equation by5 to solve for xx.
x=−255x = \frac{-25}{5}

STEP 11

Calculate the value of xx.
x=−5x = -5So, the solution to the equation is x=−5x = -5.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord