Question

d. $2(-6m - 3) = \frac{1}{2}(5m - 1)$
$-12m - 6 = \frac{1}{2}(5m - 1)$

Explanation:

Step1: Expand both sides

Left side: $2(-6m - 3)=-12m - 6$
Right side: $\frac{1}{2}(5m - 1)=\frac{5}{2}m-\frac{1}{2}$
Equation becomes: $-12m - 6=\frac{5}{2}m-\frac{1}{2}$

Step2: Eliminate fraction (multiply by 2)

$2(-12m - 6)=2(\frac{5}{2}m-\frac{1}{2})$
$-24m - 12 = 5m - 1$

Step3: Move terms with m to left, constants to right

$-24m - 5m=-1 + 12$
$-29m = 11$

Step4: Solve for m

$m=\frac{11}{-29}=-\frac{11}{29}$

Wait, but the initial note said "NO Solution" and "One Solution". Let's check again. Wait, maybe I misread. Wait, the original problem: Let's re - solve:

Wait, original equation: $2(-6m - 3)=\frac{1}{2}(5m - 1)$

First step: Distribute left: $-12m-6$, right: $\frac{5m}{2}-\frac{1}{2}$

Multiply both sides by 2 to eliminate denominator: $2\times(-12m - 6)=2\times(\frac{5m}{2}-\frac{1}{2})$

So $-24m-12 = 5m - 1$

Bring 5m to left and -12 to right: $-24m-5m=-1 + 12$

$-29m = 11$

$m=-\frac{11}{29}$, so there is one solution.

Answer:

The equation has one solution, and the solution for \(m\) is \(\boldsymbol{m = -\frac{11}{29}}\)