# How do you solve 5x- 21= 8x- 30?

Apr 23, 2016

$\implies 5 x - 8 x = 21 - 30 \implies - 3 x = - 9 \implies x = - \frac{9}{-} 3 = 3$

Apr 23, 2016

$5 x - 21 = 8 x - 30$
$9 = 3 x$
$x = 3$

or

$5 x - 21 = 8 x - 30$
$- 3 x = - 9$
$- x = - 3$
$x = 3$

#### Explanation:

To solve this equation, you must have all $x$'s on one side of the equals sign and the numbers on the other.

I always keep the $x$'s positive if I can, so here I would take the $5 x$ over to the right side of the equals sign. To cancel a $+ 5 x$ out, minus a $5 x$ from both sides of the equals sign.

$5 x - 21 = 8 x - 30$
$- 21 = 3 x - 30$

Then, cancel the $- 30$ out by adding a $30$ to both sides of the equals sign.

$- 21 = 3 x - 30$
$9 = 3 x$

Finally, because both $9$ and $3 x$ are divisible by $3$, to get the simplest form of this equation, divide both sides of the equals sign by $3$.

$9 = 3 x$

$3 = x$

$\mathmr{and}$

For the other method, use exactly the same rules as the first method. First get all the $x$'s on one side, but this time the $x$'s will be negative. This method gives exactly the same answer so the choice is yours! :)

$5 x - 21 = 8 x - 30$
$- 3 x - 21 = - 30$

I took the $8 x$ over the equals sign by adding $- 8 x$ to both sides. This gives $- 3 x$ on the left side of the equals sign.

Then do the same to the numbers. Add $- 21$ to both sides, giving:

$5 x - 21 = 8 x - 30$
$- 3 x - 21 = - 30$
$- 3 x = - 9$

As you can see, the sum at this stage is exactly the same as the other method, but this time both sides of the equals sign are negative. As an easy way to get both sides positive, simply flip the sum so it is:

$9 = 3 x$

Then do the same as the other method by dividing both sides of the equals sign by $3$.

$x = 3$