# How do you solve for x in 2x+9= 7x-1?

Mar 11, 2016

$\textcolor{g r e e n}{x = 2}$

With practice you will be able to cut out a lot of the steps I have shown you!

#### Explanation:

$\textcolor{b l u e}{\text{Method}}$

manipulate so that you have all the x's and their coefficients on one side of the = and all the numbers on the other

Manipulate the x's so that you end up with just a single x and everything else on the other side of the =

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$\textcolor{b l u e}{\text{Solving your question}}$

Given:$\text{ } \textcolor{b r o w n}{2 x + 9 = 7 x - 1}$

Keep $7 x$ where it is but move the $2 x$ as $7 x - 2 x$ is positive

Subtract $\textcolor{b l u e}{2 x}$ from both sides

$\text{ } \textcolor{b r o w n}{2 x + 9 \textcolor{b l u e}{- 2 x} = 7 x - 1 \textcolor{b l u e}{- 2 x}}$

" "color(brown)(0+9=7x-2x-1

" "color(brown)(9=5x-1

Add $\textcolor{b l u e}{1}$ to both sides

" "color(brown)(9color(blue)(+1)=5x-1color(blue)(+1)

$\text{ } \textcolor{b r o w n}{10 = 5 x + 0}$

Write as: $\textcolor{b r o w n}{5 x = 10} \text{ }$ ( this is done to match convention)

Divide both sides by $\textcolor{b l u e}{5}$

" "color(brown)( (5x)/(color(blue)(5)) =10/(color(blue)(5))

" "color(brown)( 5/5 x =2

But $\frac{5}{5} = 1$ giving

$\textcolor{g r e e n}{x = 2}$