Question

Question #b7543

Answer 1

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 = 12.5/0.8 = 15.625`

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

Answer 2

`x=15.625`

Explanation:

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

Answer 3

`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=0.8x`

Multiply both sides by 10

`125=8x`

Divide both sides by 8. This changes `8x" into "8/8x->1xx x = x`

`x=125/8`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Bit of a cheat type approach (not really)

Note that `2xx2xx2=8` so `1/2xx1/2xx1/2=1/8`

So if we apply three lots of `xx1/2` we end up with `125-:8`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Step 1"->1/2xx125=62.5)`

`color(brown)("Step 2 "->1/2xx62.5= 31.25)`

Next step has to be 'jiggled' about a bit as part of it is `1=-:2`
Note that `31.25" is the same as "30.25+1`

`color(brown)("Step 3")`

`->1/2(color(white)("d")30.25color(white)("ddd.")+color(white)("ddd")1)`

`color(brown)(->(1/2xx30.25) +(1/2xx1) =(15.125)+(0.5) = 15.625)`