# How do you solve 7( 3s + 4) = 301?

Mar 16, 2017

$s = 13$

#### Explanation:

$7 \left(3 s + 4\right) = 301$

First multiply out the brackets:

$7 \times 3 s + 7 \times 4 = 301$

$21 s + 28 = 301$

Next subtract $28$ from both sides of the $=$ sign:

$21 s + 28 - 28 = 301 - 28$

$21 s = 273$

Next divide both sides by 21 and reduce:

$\frac{{\cancel{21}}^{\textcolor{red}{1}} s}{{\cancel{21}}^{\textcolor{red}{1}}} = \frac{{\cancel{273}}^{\textcolor{red}{13}}}{{\cancel{21}}^{\textcolor{red}{1}}}$

$s = 13$

It is always a good idea (and very simple) to check your answer when you've finished.

Replace the constant with the value you found in the original formula. So in this case:

$7 \left(3 \times 13 + 4\right) = 301$

$7 \left(39 + 4\right) = 301$

$7 \times 43 = 301$

$301 = 301$

The left hand side (LHS) and right hand side (RHS) of the equal's match, proving the answer correct.

Mar 16, 2017

$s = 13$

#### Explanation:

The first step is to distribute the bracket on the left side.

$\Rightarrow 21 s + 28 = 301$

subtract 28 from both sides.

$21 s \cancel{+ 28} \cancel{- 28} = 301 - 28$

$\Rightarrow 21 s = 273$

divide both sides by 21

$\frac{\cancel{21} s}{\cancel{21}} = \frac{273}{21}$

$\Rightarrow s = 13 \text{ is the solution}$

Mar 16, 2017

Just another approach!

$s = 13$

#### Explanation:

The objective is to work you way to getting just 1 of s and for it to be on its own on one side of the = and everything else on the other side.

Isolating the $\underline{\text{'group'}}$ of values that has s in it- divide both sides by 7

$3 s + 4 = \frac{301}{7}$

Isolating 3s: subtract 4 from both sides

$3 s = \frac{301}{7} - 4$

Final isolation step: divide both sides by 3

$s = \frac{301}{3 \times 7} - \frac{4}{3}$

$s = \frac{301}{21} - \frac{4}{3}$

But $3 \times 7 = 21$

$\textcolor{g r e e n}{s = \frac{301}{21} - \left[\frac{4}{3} \textcolor{red}{\times 1}\right]}$

$\textcolor{g r e e n}{s = \frac{301}{21} - \left[\frac{4}{3} \textcolor{red}{\times \frac{7}{7}}\right]}$

$s = \frac{301}{21} - \frac{28}{21}$

$s = \frac{273}{21} = 13$