# How do you solve 7(w+1)=5(2w-3)+1?

Jul 14, 2016

$w = 7$

#### Explanation:

Start by expanding both sides of the equation:

$7 \left(w + 1\right) = 5 \left(2 w - 3\right) + 1$

$= 7 w + 7 = 10 w - 15 + 1$

Then we simplify by getting the terms with $w$ on one side and the integers on the other:

$7 w - 7 w + 7 + 14 = 10 w - 7 w - 14 + 14$

Therefore,

$21 = 3 w$

By dividing both sides by $3$ we see that:

$\frac{21}{3} = 3 \frac{w}{3} = 7 = w$

You can verify this by putting $7$ back into the original equations:

$7 \left(7 + 1\right) = 5 \left(14 - 3\right) + 1$

$= 7 \left(8\right) = 5 \left(11\right) + 1$

$= 56 = 55 + 1$