Question

Solve the following equation and check your results: $\frac{2x}{3}+1=\frac{7x}{15}+3$

Answer 1

Step 1: Calculate the value of $x$.

Cross multiply the terms, take the similar terms on one side and then calculate the value of $x$.

Therefore,

$\begin{array}{c}\frac{2x}{3}+1=\frac{7x}{15}+3\\ \frac{2x}{3}-\frac{7x}{15}=3-1\\ \frac{2x\times 5}{3\times 5}-\frac{7x\times 1}{15\times 1}=2\\ \frac{10x}{15}-\frac{7x}{15}=2\\ \frac{3x}{15}=2\\ x=\frac{15\times 2}{3}\\ x=5\times 2\\ x=10\end{array}$

Step 2: Verify the equation for $x=10$.

Apply $x=10$in the equation $\frac{2x}{3}+1=\frac{7x}{15}+3$.

Solve LHS.

$\begin{array}{c}\frac{2\times 10}{3}+1=\frac{20}{3}+1\\ =\frac{20+3}{3}\\ =\frac{23}{3}\end{array}$

Solve RHS.

$\begin{array}{c}\frac{7\times 10}{15}+3=\frac{14}{3}+3\\ =\frac{14+9}{3}\\ =\frac{23}{3}\end{array}$

Therefore, LHS is equal to RHS.

Hence, the value of $x$is verified for the equation $\frac{2x}{3}+1=\frac{7x}{15}+3$.