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

Apr 6, 2018

All real numbers or $\left(- \infty , \infty\right)$ 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

$- 3 x - 11 = - 3 x - 11$

Since both sides of the equation are the same, that means that there are infinitely many solutions, or all real numbers, or $\left(- \infty , \infty\right)$.

Apr 6, 2018

There are infinitely many solutions for $x$.

#### Explanation:

1. Distribute
$4 x + 10 - 7 x - 21 = - 15 + 5 x - 8 x + 4$
PAY ATTENTION TO NEGATIVE SIGNS
2. Combine like terms on both sides of the equation
$- 3 x - 11 = - 3 x - 11$
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.
Apr 6, 2018

All real numbers or $\left(- \infty , \infty\right)$

Here's how I did it:

#### Explanation:

$2 \left(2 x + 5\right) - 7 x - 21 = 5 \left(- 3 + x\right) - 8 x + 4$

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 $2 \left(2 x + 5\right)$:
$2 \cdot 2 x = 4 x$

$2 \cdot 5 = 10$

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

Now let's look at $5 \left(- 3 + x\right)$:
$5 \cdot - 3 = - 15$

$5 \cdot x = 5 x$

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

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

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

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

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 $\left(- \infty , \infty\right)$.

Hope this helps!