Question

Solve [(2x / 3)+ 1 )] =[ (7x / 15) + 3 ] and find the value of x.​

Answer 1

Question

Find the value of 'x' in this equation ⇒ $\frac{2x}{3}+1=\frac{7x}{15}+3$

$\rule{300}{1}$

Answer

Let's solve your equation step-by-step.

$\frac{2x}{3}+1=\frac{7x}{15}+3$

Step 1: Simplify both sides of the equation.

$\frac{2}{3}x+1=\frac{7}{15}x+3$

Step 2: Subtract $\frac{7}{15}x$ from both sides.

$\frac{2}{3}x+1 - \frac{7}{15}x =\frac{7}{15}x+3- \frac{7}{15}x$

$\frac{1}{5}x+1=3$

Step 3: Subtract 1 from both sides.

$\frac{1}{5}x+1-1=3-1$

$\frac{1}{5}x=2$

Step 4: Multiply both sides by 5.

$5\times \frac{1}{5}x=5\times 2$

$x=10$

Let's verify if x=10.

Method 1

Step 1: Simplify the equation.

$\frac{2x}{3}+1=\frac{7x}{15}+3$

$\frac{2}{3}x+1=\frac{7}{15}x+3$

Step 2: Subtract $\frac{7}{15}x$ from both sides.

$\frac{2}{3}x+1 - \frac{7}{15}x =\frac{7}{15}x+3- \frac{7}{15}x$

$\frac{1}{5}x+1=3$

Step 3: Subtract 1 from both sides.

$\frac{1}{5}x+1-1=3-1$

$\frac{1}{5}x=2$

Step 4: Put the value of 'x' and verify.

$\frac{1}{5}x=2$

$\frac{1}{5} \times 10 =2$

$2=2$

Method 2

Step 1: Put the value of 'x' and make sure LHS=RHS

$\frac{2x}{3}+1=\frac{7x}{15}+3$

$\frac{2\times 10 }{3}+1=\frac{7\times 10 }{15}+3$

$\frac{20 }{3}+1=\frac{70 }{15}+3$

$\frac{20 }{3}+\frac{1\times 3}{1\times 3 } =\frac{14 }{3}+\frac{3 \times 3 }{1 \times 3}$

$\frac{20 }{3}+\frac{3}{3 } =\frac{14 }{3}+\frac{9 }{3}$

$\frac{23 }{3}=\frac{23}{3}$

∴LHS=RHS

∴ x=10 in the equation ⇒  $\bf \frac{2x}{3}+1=\frac{7x}{15}+3$

$\rule{300}{1}$