Question

How do you solve `2( 2x + 5) - 7x - 21= 5( - 3+ x ) - 8x + 4`?

Answer 1

All real numbers or `(-oo, oo)` or infinitely many solutions

Explanation:

Expand and collect like terms:

`2(2x+5) − 7x − 21 = 5(−3+x) − 8x + 4`

`4x + 10 − 7x − 21 = -15 + 5x) − 8x + 4`

`-3x - 11 = -3x - 11`

Since both sides of the equation are the same, that means that there are infinitely many solutions, or all real numbers, or `(-oo, oo)`.

Answer 2

There are infinitely many solutions for `x`.

Explanation:

1. Distribute
   `4x+10-7x-21=-15+5x-8x+4`
   PAY ATTENTION TO NEGATIVE SIGNS
2. Combine like terms on both sides of the equation
   `-3x-11=-3x-11`
3. Since we now have both sides of the equation looking exactly the same we know that `x=x` and therefore know that `x` can equal anything.

Answer 3

All real numbers or `(-oo, oo)`

Here's how I did it:

Explanation:

`2(2x+5) - 7x - 21 = 5(-3 + x) - 8x + 4`

The first thing we want to do is distribute or multiply the value outside of the parenthesis to everything inside it. Let's take a look at `2(2x+5)`:
`2 * 2x = 4x`

`2 * 5 = 10`

When we combine this together we get `4x + 10`

Now let's look at `5(-3 + x)`:
`5 * -3 = -15`

`5 * x = 5x`

When we combine this together we get `5x - 15`

Now let's put these back into the equation:
`4x + 10 - 7x - 21 = 5x - 15 - 8x + 4`

Now we simplify by combining like terms:
`-3x - 11 = -3x - 11`

Add `11` to both sides of the equation:
`-3x = -3x`

Divide both sides by `-3`:
`x = x`

Since we know that `x = x` is true, since a value equals to itself, that means the answer is all real numbers, or `(-oo, oo)`.

Hope this helps!