Questions: Solve for x: 1/4(x+2) = 1/2(3x-4)

Transcript text: Solve for $\mathrm{x}: \quad \frac{1}{4}(x+2)=\frac{1}{2}(3 x-4)$

Solution

Solution Steps

Step 1: Eliminate the fractions

Multiply both sides of the equation by 4 to eliminate the denominators: \[ 4 \cdot \frac{1}{4}(x+2) = 4 \cdot \frac{1}{2}(3x-4) \] Simplify: \[ (x+2) = 2(3x-4) \]

Step 2: Expand the right side

Expand the right side of the equation: \[ x + 2 = 6x - 8 \]

Step 3: Collect like terms

Move all terms involving $ x $ to one side and constants to the other: \[ x - 6x = -8 - 2 \] Simplify: \[ -5x = -10 \]

Step 4: Solve for $ x $

Divide both sides by $-5$ to solve for $ x $: \[ x = \frac{-10}{-5} = 2 \]

Final Answer

$\boxed{x = 2}$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >