3÷2(2x−1)= 1÷4(5x−3)

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for the new equation.

The equation is:

\frac{3}{2}(2x-1) = \frac{1}{4}(5x-3)

Distribute the numbers on both sides of the equation.
$\left(\frac{3}{2} \times 2x\right) - \left(\frac{3}{2} \times 1\right) = \left(\frac{1}{4} \times 5x\right) - \left(\frac{1}{4} \times 3\right)$ $3x - \frac{3}{2} = \frac{5x}{4} - \frac{3}{4}$
Eliminate the denominators by multiplying the entire equation by the least common multiple (LCM) of the denominators.
The LCM of 2 and 4 is 4.
Multiply every term by 4:
$4(3x) - 4\left(\frac{3}{2}\right) = 4\left(\frac{5x}{4}\right) - 4\left(\frac{3}{4}\right)$ $12x - 6 = 5x - 3$
Collect all terms with $x$ on one side and constant terms on the other side.
Subtract $5x$ from both sides:
$12x - 5x - 6 = -3$ $7x - 6 = -3$
Add 6 to both sides:
$7x = -3 + 6$ $7x = 3$
Solve for $x$ .
Divide both sides by 7:
$x = \frac{3}{7}$
The final answer is $\frac{3}{7}$ .

Answer