# How do you solve 7x - 9 = -10 + 4x?

Mar 27, 2018

$x = - \frac{1}{3}$

#### Explanation:

$7 x - 9 = - 10 + 4 x | \textcolor{b l u e}{+ 9 - 4 x}$
$7 x \cancel{- 9} \textcolor{b l u e}{\cancel{+ 9} - 4 x} = - 10 \cancel{+ 4 x} \textcolor{b l u e}{+ 9 \cancel{- 4 x}}$
$3 x = - 1 | \textcolor{red}{: 3}$
$\frac{\cancel{3} x}{\textcolor{red}{\cancel{3}}} = \frac{- 1}{\textcolor{red}{3}}$
$x = - \frac{1}{3}$

Mar 27, 2018

Rearrange the equation so all x-terms are on one side and constants are on the other, then solve for x. This gives you $x = - \frac{1}{3}$

#### Explanation:

First, we should rearrange the constants so they are all on one side. I prefer having constants on the Right Hand Side (RHS) as opposed to the Left Hand Side (LHS).

We can rearrange by adding/subtracting values from both sides of the equation.

For this problem, we will first add 9 to both sides of the equation. This will eliminate the -9 from the LHS, and effectively move its value to the RHS:

$7 x \cancel{- 9 + 9} = - 10 + 4 x + 9$

$7 x = - 1 + 4 x$

Now, we'll move the $4 x$ term to the LHS. We will do this by subtracting $4 x$ from both sides:

$7 x - 4 x = - 1 \cancel{+ 4 x - 4 x}$

$\left(7 - 4\right) x = - 1 \Rightarrow 3 x = - 1$

Finally, divide through by any coefficients that $x$ is multiplied by. In this case, that coefficient is 3:

$\frac{3 x}{3} = - \frac{1}{3}$

$\textcolor{red}{x = - \frac{1}{3}}$

Mar 27, 2018

$7 x - 9 = - 10 + 4 x$

$3 x - 9 = - 10$

$3 x = - 1$

$x = - \frac{1}{3}$

#### Explanation:

You can do operations to one side of an equation, including but not limited to with variables, if you also do it to the other side. Through this you can eliminate parts of both sides to solve the equation to get x = ?.

Line 1 to 2: taking away $4 x$ from both sides
Line 2 to 3: adding $9$ to both sides
Line 3 to 4: dividing both sides by $3$