# Question #b7543

Jan 10, 2018

#### Answer:

To solve for x, divide by 0.8.

$x = 15.625$

#### Explanation:

This is a linear equation.

To solve we divide by the coefficient (0.8) in this case.

$\therefore x = \frac{12.5}{0.8} = 15.625$

If you didn't have a calculator, leaving it as a fraction is fine :) .

Jan 10, 2018

#### Answer:

$x = 15.625$

#### Explanation:

Divide each side by 0.8
Since we are trying to find out what $x$ equals and not what $0.8 x$ equals, we need to get rid of the 0.8. Dividing a number by itself always results in 1.

Jan 14, 2018

#### Answer:

$15.625$

A none calculator 'cheat type' approach
Takes longer to explain than do the actual calculations. Also demonstrates 'distributive' property of multiplication in step 3.

#### Explanation:

If it is the decimals that are giving you a problem this is a way round it (for this question).

Given: $12.5 = 0.8 x$

Multiply both sides by 10

$125 = 8 x$

Divide both sides by 8. This changes $8 x \text{ into } \frac{8}{8} x \to 1 \times x = x$

$x = \frac{125}{8}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bit of a cheat type approach (not really)

Note that $2 \times 2 \times 2 = 8$ so $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$

So if we apply three lots of $\times \frac{1}{2}$ we end up with $125 \div 8$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Step 1} \to \frac{1}{2} \times 125 = 62.5}$

$\textcolor{b r o w n}{\text{Step 2 } \to \frac{1}{2} \times 62.5 = 31.25}$

Next step has to be 'jiggled' about a bit as part of it is $1 = \div 2$
Note that $31.25 \text{ is the same as } 30.25 + 1$

$\textcolor{b r o w n}{\text{Step 3}}$

$\to \frac{1}{2} \left(\textcolor{w h i t e}{\text{d")30.25color(white)("ddd.")+color(white)("ddd}} 1\right)$

$\textcolor{b r o w n}{\to \left(\frac{1}{2} \times 30.25\right) + \left(\frac{1}{2} \times 1\right) = \left(15.125\right) + \left(0.5\right) = 15.625}$