Question

solve for w.
$4+\frac{3}{w-2}=\frac{7}{w-2}$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$w = \square$

Explanation:

Step1: Eliminate the denominator

Multiply both sides of the equation \(4+\frac{3}{w - 2}=\frac{7}{w - 2}\) by \(w - 2\) (note that \(w
eq2\) to avoid division by zero). We get \(4(w - 2)+3 = 7\).

Step2: Expand and simplify

Expand the left - hand side: \(4w-8 + 3=7\), which simplifies to \(4w-5 = 7\).

Step3: Solve for w

Add 5 to both sides: \(4w=7 + 5=12\). Then divide both sides by 4: \(w=\frac{12}{4}=3\).
We need to check if \(w = 3\) is valid. Substitute \(w = 3\) into the original equation's denominator \(w-2=3 - 2=1
eq0\), so \(w = 3\) is a valid solution.

Answer:

\(w = 3\)