Question #248ba

Mar 17, 2017

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

Explanation:

$\textcolor{b l u e}{\text{Reduce the fractions}}$

$\frac{{\cancel{9}}^{\textcolor{red}{1}} \left(1 - 2 x\right)}{{\cancel{9}}^{\textcolor{red}{1}} \left(1 + 2 x\right)} - \frac{{\cancel{7}}^{\textcolor{red}{1}} \left(2 x\right)}{{\cancel{7}}^{\textcolor{red}{1}} \left(1 + 2 x\right)} = 3$

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

$\textcolor{b l u e}{\text{Carry out the subtraction of the fractions}}$

Because the denominator (the bottom number) is the same for each fraction, you simply subtract the second numerator (top number of the fraction) from the first:

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

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

$\textcolor{b l u e}{\text{Remove the denominator}}$

By multiplying both sides of the equals sign by $1 + 2 x$, we can remove the denominator:

$\frac{1 - 4 x}{\cancel{1 + 2 x}} ^ \textcolor{red}{1} \times \left({\cancel{1 + 2 x}}^{\textcolor{red}{1}}\right) = 3 \left(1 + 2 x\right)$

$1 - 4 x = 3 + 6 x$

$\textcolor{b l u e}{\text{Rearrange}}$

Add $4 x$ to both sides and subtract $3$ from both sides gives:

$1 - 4 x + 4 x - 3 = 3 + 6 x + 4 x - 3$

$\textcolor{b l u e}{\text{Collect like terms}}$

$1 - 3 = 6 x + 4 x$

$- 2 = 10 x$

$\textcolor{b l u e}{\text{Find the answer}}$

Divide both sides through by 10, to give:

$- \frac{2}{10} = x$

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