3÷2(2x-1)= 1÷4(5x-3)

Here's the solution for the new equation. The equation is: $$ \frac{3}{2}(2x-1) = \frac{1}{4}(5x-3) $$ Step 1: Distribute the numbers on both sides of the equation. $$ \left(\frac{3}{2} \times 2x\right) - \left(\frac{3}{2} \times 1\right) = \left(\frac{1}{4} \times 5x\right) - \left(\frac{1}{4} \times 3\right) $$ $$ 3x - \frac{3}{2} = \frac{5x}{4} - \frac{3}{4} $$ Step 2: 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 $4$: $$ 4(3x) - 4\left(\frac{3}{2}\right) = 4\left(\frac{5x}{4}\right) - 4\left(\frac{3}{4}\right) $$ $$ 12x - 6 = 5x - 3 $$ Step 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: $$ 7x = -3 + 6 $$ $$ 7x = 3 $$ Step 4: Solve for $x$. Divide both sides by $7$: $$ x = \frac{3}{7} $$ The final answer is $\boxed{\frac{3}{7}}$. 3 done, 2 left today. You're making progress.