# How do you solve 3x-51=-2x+59?

Jan 12, 2018

$x = 22$

#### Explanation:

1) Combine Like terms by transposition of terms. [Remember to reverse the signs when transposing]

$3 x - 51 = - 2 x + 59$

By combining like terms, you should get

$3 x + 2 x = 110 + 51$

$\Rightarrow 5 x = 110$

2) Divide by $5$ on both sides and you will get the answer.

$5 x = 110$

$\Rightarrow x = 22$

22

#### Explanation:

This is a topic of mathematical transpositions. The main goal of transposing is grouping variables and constants on different sides for easier evaluation without disrupting the equality of the whole system/equation.

For this example, we can group all terms with the $x$ variables at one side, let's say the left side and also group all constants or terms without variables on the right side.

This would specifically mean that $- 2 x$ will be transposed onto the left side and $- 51$ will be transposed onto the right side. As a result, the equation will yield:
$3 x + 2 x = 59 + 51$

Simplifying,
$5 x = 110$

Solving for $x$;
$x = \frac{110}{5} = 22$

Take note that the transposed terms $- 2 x$ and $- 51$ have changed their signs after transposing. This is true to maintain the equality of the whole equation.

For example,
$5 + 8 = 13$
If we transpose $8$ onto the other side of the equation, the whole equation becomes
$\left[5 = 13 - 8\right]$ or $\left[5 = - 8 + 13\right]$
And we can see that the equality of the whole equation is maintained. In essence, the mathematical operation performed in the transposition can be done by subtracting $8$ (or adding $- 8$) on both sides:
$\left(5 + 8\right) - 8 = \left(13\right) - 8$
$5 = 13 - 8$