# How do you solve 7- 3( 5t - 10) = 67?

Sep 21, 2016

Distribute the $- 3$ first.

#### Explanation:

You may be tempted to subtract $7$ and $3$ but that is the wrong thing to do. Subtracting $3$ is the same thing as a negative $3$, so we should distribute the $- 3$ to everything in the parenthesis.

Distributing the $- 3$:

• Multiply $- 3$ by $5 t$ to get $- 15 t$ and multiply $- 3$ by $- 10$ to get positive $30$

$7 - 15 t + 30 = 67$

The $7$ and the $30$ both have no variable, so these can be combined.

$7 + 30 = 37$

Now we're left with

$37 - 15 t = 67$

The next step would be to subtract $37$ from both sides. Remember, the goal with these kinds of equations is to isolate the variable to get our answer. $37 - 37$ cancels out, and $67 - 37$ is $30$.

We're left with

$- 15 t = 30$

When a variable term is equal to a constant term, you always divide by the coefficient of the variable (number in front of variable).

The coefficient is $- 15$. Dividing $- 15 t$ by $- 15$ will just leave $t$, and $\frac{30}{- 15}$ is equal to $- 2$. This means

$t = - 2$

I'm in the 9th grade and I did a problem like this today :)