# What are are two consecutive integers, such that seven times the larger minus three times the smaller is 95?

Mar 9, 2018

The numbers are $22$ and $23$

#### Explanation:

Alright, to solve a problem like this, we need to read and define as we go. Let me explain.

So we know that there are two consecutive integers. They can be $x$ and $x + 1$. Since their consecutive, one has to be $1$ number higher (or lower) than the other.

Ok, so first we need "seven times the larger"

$7 \left(x + 1\right)$

Next, we need to "minus three times the smaller"

$7 \left(x + 1\right) - 3 x$

Is equal to "$95$"

$7 \left(x + 1\right) - 3 x = 95$

Alright! There's the equation, now we just need to solve for $x$! First we are going to get everything on one side and distribute the $7$.

$= 7 x + 7 - 3 x - 95$

$= 4 x - 88$

Pull out a $4$

$= 4 \left(x - 22\right)$

Now that we have two terms, we can set them both equal to $0$ and solve.

$4 \ne 0$

This can never be true, lets move to the next term

$\left(x - 22\right) = 0$

$x = 22$

That's it! So your two consecutive numbers are $22$ and $23$!

If you want to check this, just put $22$ in place of the $x$ and $23$ in place of the $\left(x + 1\right)$ in the equation we made above!

Hope this helps!
~Chandler Dowd