Problem of the Week

Updated at Nov 14, 2022 3:07 PM

How would you solve the equation \(\frac{x+2}{3}+\frac{4x}{5}=\frac{26}{5}\)?

Below is the solution.



\[\frac{x+2}{3}+\frac{4x}{5}=\frac{26}{5}\]

1
Multiply both sides by \(15\) (the LCM of \(3, 5\)).
\[5(x+2)+12x=78\]

2
Expand.
\[5x+10+12x=78\]

3
Simplify  \(5x+10+12x\)  to  \(17x+10\).
\[17x+10=78\]

4
Subtract \(10\) from both sides.
\[17x=78-10\]

5
Simplify  \(78-10\)  to  \(68\).
\[17x=68\]

6
Divide both sides by \(17\).
\[x=\frac{68}{17}\]

7
Simplify  \(\frac{68}{17}\)  to  \(4\).
\[x=4\]

Done
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