# How do you solve 3(x+5) +6 = 15?

Jun 7, 2016

color(blue)(x=-2

#### Explanation:

$3 \left(x + 5\right) + 6 = 15$

$\textcolor{b l u e}{\left(3\right)} \cdot \left(x + 5\right) + 6 = 15$

$\textcolor{b l u e}{\left(3\right)} \cdot \left(x\right) + \textcolor{b l u e}{\left(3\right)} \cdot \left(5\right) + 6 = 15$

$3 x + 15 + 6 = 15$

$3 x + 21 = 15$

$3 x = 15 - 21$

$3 x = - 6$

$x = \frac{- 6}{3}$

color(blue)(x=-2

Jun 7, 2016

Just in case you need further explanation

$x = - 2$

#### Explanation:

Consider $3 \left(x + 5\right)$ This means that you have 3 lots of $\left(x + 5\right)$

Which is: $x + 5$
$\text{ } x + 5$
$\text{ "ul(x+5) " "larr} a \mathrm{dd}$
$\text{ } 3 x + 15$

$\textcolor{g r e e n}{\text{Basically you multiply everything inside the brackets by 3}}$

So $\text{ "color(brown)(3(x+5)+6=15)" "color(blue)(->" } 3 x + 15 + 6 = 15$

$3 x + 21 = 15$

'~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{g r e e n}{\text{To get rid of the 21 on the left subtract 21 from both sides}}$

$3 x + 21 - 21 = 15 - 21$

$3 x + 0 = - 6$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{g r e e n}{\text{To get rid of the 3 from "3x" divide both sides by 3}}$

$\frac{3}{3} \times x = - \frac{6}{3}$

But $\frac{3}{3} = 1 \text{ and } 1 \times x = x$

$x = - 2$