Question

If $2x+1=-x+3$, what is the value of $\left(\frac{2}{3}\right)x+\frac{1}{3}$?

• A. $1$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{7}{9}$

Answer 1

The correct option is D $\frac{7}{9}$

First we will find the value of $x$ from the given equation.
$\Rightarrow 2x+1=-x+3$
$\Rightarrow 2x+x=3-1$
$\Rightarrow 3x=2$
$\Rightarrow x=\frac{2}{3}$
To find the value of the equation by substituting the value of $x=\frac{2}{3}$
$\Rightarrow \left(\frac{2}{3}\right)x+\frac{1}{3}=$ $\frac{2}{3}\times \frac{2}{3}+\frac{1}{3}$
$=\frac{4}{9}+\frac{1}{3}$
$=\frac{9\times 1+4\times 3}{27}=\frac{21}{27}$
$=\frac{21}{27}=\frac{7}{9}$
Hence, option D is the correct answer.