Studdy AI Logo
Math  /  Algebra

QuestionSolve for xx. 5x8−2=7x12\frac{5 x}{8}-2=\frac{7 x}{12}
Simplify your answer as much as possible.

Studdy Solution

STEP 1

1. The equation 5x8−2=7x12\frac{5x}{8} - 2 = \frac{7x}{12} is a linear equation in one variable.
2. The goal is to solve for xx.
3. We will need to perform operations to isolate xx on one side of the equation.

STEP 2

1. Eliminate fractions by finding a common denominator.
2. Move all terms involving xx to one side of the equation.
3. Solve for xx by isolating it.
4. Simplify the solution.

STEP 3

To eliminate the fractions, find the least common denominator (LCD) of 8 and 12, which is 24.
Multiply every term in the equation by 24 to clear the fractions:
24(5x8)−24(2)=24(7x12) 24 \left(\frac{5x}{8}\right) - 24(2) = 24 \left(\frac{7x}{12}\right)

STEP 4

Simplify each term:
3⋅5x−48=2⋅7x 3 \cdot 5x - 48 = 2 \cdot 7x
15x−48=14x 15x - 48 = 14x

STEP 5

Move all terms involving xx to one side by subtracting 14x14x from both sides:
15x−14x−48=0 15x - 14x - 48 = 0

STEP 6

Simplify the equation:
x−48=0 x - 48 = 0

STEP 7

Add 48 to both sides to isolate xx:
x=48 x = 48

STEP 8

The solution is already simplified. Therefore, the solution is:
48 \boxed{48}

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