. Two times a number plus 6 is three less than one fifth of the number. What is the number?

Jun 16, 2018

$x = - 5$

Explanation:

Let the unknown number be $x$

From statement..

$2 \times x + 6 = \left(\frac{1}{5} o f x\right) - 3$

The word times is represented by multiplication..

The word plus is represented by addition..

The word is is represented by equal to..

The word less than is represented by subtraction..

The word of can be represented by multiplication..

Now solving the statement;

$2 x + 6 = \left(\frac{1}{5} \times x\right) - 3$

$2 x + 6 = \frac{1}{5} x - 3$

$2 x + 6 = \frac{x}{5} - 3$

$\frac{2 x}{1} + \frac{6}{1} = \frac{x}{5} - \frac{3}{1}$

Multiply through by their LCM, which is $5$

$5 \left(\frac{2 x}{1}\right) + 5 \left(\frac{6}{1}\right) = 5 \left(\frac{x}{5}\right) - 5 \left(\frac{3}{1}\right)$

$10 x + 30 = \cancel{5} \left(\frac{x}{\cancel{5}}\right) - 15$

$10 x + 30 = x - 15$

Collecting like terms;

$10 x - x = - 15 - 30$

$9 x = - 45$

$x = - \frac{45}{9}$

$x = - 5$