Question

How do you solve `2.2x - 5= 2( 1.4x + 3)`?

Answer 1

`x=-18.33=-55/3`

Explanation:

Use order of operations (PEMDAS).
`color(blue)P`araentheses
`color(blue)E`xponents
`color(blue)M`ultiplication/`color(blue)D`ivision
`color(blue)A`ddition/`color(blue)S`ubtraction

1. Solve inside parentheses first. Since `(1.4x+3)` cannot be simplified any more, skip this step.

2. There are no exponents, so skip this step.

3. Multiply `2(1.4x+3)` by distributing the `2`. There is no division, so do not worry about dividing anything.
   `2.2x - 5= color(red)(2(1.4x + 3))`
   `2.2x - 5= color(red)(2(1.4x)+2(3))`
   `2.2x - 5= color(red)(2.8x+6)`

4. Since we cannot simplify the equation by adding or subtracting, skip this step.

5. Isolate and solve for `x`.
   `color(red)(-0.6x)-5=6`
   `-0.6x=color(red)11`
   `x=-11/0.6=-18.33`

EXTRA STEP: If your teacher wants the answer in fraction form, technically `-11/0.6` is not correct because we cannot have a decimal in a fraction. Follow the steps below to rewrite it:
`-11/(6/10)=-11/1-:6/10=-11/1*10/6=-110/6=-55/3`