Question

2/3w - 1/4 = 2/3 (w - 1/4)

Answer 1

Given problem is

$\frac{2}{3}w-\frac{1}{4}=\frac{2}{3}\left(w-\frac{1}{4}\right)$

Here unknown variable is w so we will solve this equation for w.

Common denominator for given denominators 3 and 4 is 12 so we can multiply both sides by 12 so that we can cancel out all the fractions

$\frac{2}{3}w\cdot12-\frac{1}{4}\cdot12=\frac{2}{3}\cdot12\left(w-\frac{1}{4}\right)$

$\frac{24}{3}w-\frac{12}{4}=\frac{24}{3}\left(w-\frac{1}{4}\right)$

$8w-3=8\left(w-\frac{1}{4}\right)$

$8w-3=8w-\frac{8}{4}$

$8w-3=8w-2$

$8w-8w=3-2$

$0=1$

We know that 0=1 is not possible

Hence there is no solution for w.

Answer 2

Answer:

No solution

Step-by-step solution:

We are given an expression:

$\frac{2}{3} w-\frac{1}{4} =\frac{2}{3} (w-\frac{1}{4} )$

We have only one variable $w$ so we will make $w$ the subject and solve for it.

$\frac{2}{3} w-\frac{1}{4} =\frac{2}{3} (w-\frac{1}{4} )$

Solving the brackets first to get:

$\frac{2}{3} w -\frac{1}{4} =\frac{2}{3} -\frac{1}{6}$

Taking LCM on both sides to get:

$\frac{8w-3}{12} =\frac{4w-3}{6}$

By cross multiplication:

$6(8w-3)=12(4w-3)$

$48w-18 = 48w -36$

$48w - 49w -18 + 36 = 0$

$w$ gets cancelled so we are left with $18\neq 0$

Therefore, $w$ has no solution.