Question

solve for w.
20 = \frac{8w + 9}{5} + \frac{8w - 7}{7}
simplify your answer as much as possible.
w = \boxed{}

Explanation:

Step1: Find common denominator

The denominators are 5 and 7, so the common denominator is \( 5\times7 = 35 \). Multiply each term by 35 to eliminate fractions:
\( 35\times20 = 35\times\frac{8w + 9}{5}+35\times\frac{8w - 7}{7} \)
Simplify each term: \( 700 = 7(8w + 9)+5(8w - 7) \)

Step2: Expand brackets

Expand the right - hand side:
\( 700=56w + 63+40w-35 \)

Step3: Combine like terms

Combine the \( w \) terms and the constant terms:
\( 700=(56w + 40w)+(63 - 35) \)
\( 700 = 96w+28 \)

Step4: Isolate the variable term

Subtract 28 from both sides:
\( 700 - 28=96w \)
\( 672 = 96w \)

Step5: Solve for w

Divide both sides by 96:
\( w=\frac{672}{96}=7 \)

Answer:

\( w = 7 \)