Question

$\frac{2x}{3}-\frac{x-1}{6}+\frac{7x-1}{4}=2\frac{1}{6}$

Hence, find the value of $x$ and $a$, if $\frac{1}{a}+5x=8.$

• A. $x=2$ and $a=\frac{1}{2}$
• B. $x=3$ and $a=\frac{1}{4}$
• C. $x=4$ and $a=\frac{1}{5}$
• D. $x=1$ and $a=\frac{1}{3}$

Answer 1

The correct option is D $x=1$ and $a=\frac{1}{3}$

Given equation can be written as

$\frac{2x}{3}-\frac{x-1}{6}+\frac{7x-1}{4}=\frac{13}{6}$

$\frac{4\left(2x\right)-2(x-1)+3(7x-1)}{12}=\frac{2\left(13\right)}{12}$

$8x-2x+2+21x-3=26\Rightarrow 27x=27$

$\therefore x=1$

Now, $\frac{1}{a}+5x=8$

$\frac{1}{a}+5=8$

$\frac{1}{a}=3\Rightarrow a=\frac{1}{3}$