Question

How do you solve `2(2+3)+4x=2(2x+2)+6`?

Answer 1

All real numbers or `(-oo, oo)` in interval notation.

Explanation:

`2(2+3) + 4x = 2(2x+2) + 6`

First, simplify `2(2+3)`:
`color(blue)(2(2+3) = 2(5) = 10)`

Put it back into the equation:
`10 + 4x = 2(2x+2) + 6`

Next, use the distributive property to simplify `2(2x+2)`:

Following this image, we know that:
`color(blue)(2(2x+2) = (2 * 2x) + (2 * 2) = 4x + 4)`

Put it back into the equation:
`10 + 4x = 4x + 4 + 6`

Add `4+6 = 10`:
`10 + 4x = 4x + 10`

Subtract `color(blue)(4x)` from both sides of the equation:
`10 + 4x quadcolor(blue)(-quad4x)= 4x + 10 quadcolor(blue)(-quad4x)`

`10 = 10`

Oh no! Our variables are gone now. Now we see if this equation is true. It is true that `10 = 10`, meaning that the answer is All real numbers or `(-oo, oo)` in interval notation.

Hope this helps!