Question

b. \\(\frac{x - 5}{-2} = \frac{x - 1}{-3}\\) hint (b): start by multiplying both sides by a common multiple to remove the fractions.

Explanation:

Step1: Multiply by common denominator

Multiply both sides by $6$ (the least common multiple of 2 and 3):
$$6\times\frac{x-5}{2}=6\times\frac{x-1}{3}$$

Step2: Simplify both sides

Cancel denominators and simplify:
$$3(x-5)=2(x-1)$$

Step3: Expand the parentheses

Distribute the coefficients:
$$3x-15=2x-2$$

Step4: Isolate the variable $x$

Subtract $2x$ from both sides, then add 15 to both sides:
$$3x-2x=-2+15$$

Step5: Calculate the final value

Simplify to solve for $x$:
$$x=13$$

Answer:

$x=13$