Studdy AI Logo
Math  /  Algebra

QuestionSolve the rational equ 1.) 4−3x6=3x−44\frac{4-3 x}{6}=\frac{3 x-4}{4}

Studdy Solution

STEP 1

1. The equation 4−3x6=3x−44\frac{4-3x}{6} = \frac{3x-4}{4} involves rational expressions.
2. To solve for xx, we need to eliminate the fractions by finding a common denominator or cross-multiplying.
3. The final solution should provide the value(s) of xx that satisfy the equation.

STEP 2

1. Cross-multiply to eliminate the fractions.
2. Simplify the resulting equation.
3. Solve the linear equation for xx.

STEP 3

Cross-multiply to eliminate the fractions:
(4−3x)⋅4=(3x−4)⋅6 (4 - 3x) \cdot 4 = (3x - 4) \cdot 6

STEP 4

Distribute the terms on both sides of the equation:
4⋅4−4⋅3x=6⋅3x−6⋅4 4 \cdot 4 - 4 \cdot 3x = 6 \cdot 3x - 6 \cdot 4
This simplifies to:
16−12x=18x−24 16 - 12x = 18x - 24

STEP 5

Move all terms involving xx to one side and constants to the other:
16+24=18x+12x 16 + 24 = 18x + 12x
This simplifies to:
40=30x 40 = 30x

STEP 6

Solve for xx by dividing both sides by 30:
x=4030 x = \frac{40}{30}
Simplify the fraction:
x=43 x = \frac{4}{3}
Solution: The value of xx that satisfies the equation is:
x=43 x = \frac{4}{3}

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