# How do you solve (3w+8)/2=25?

Jul 21, 2016

w = 14

#### Explanation:

$\frac{3 w + 8}{2} = 25$

$3 w + 8 = 50$

$3 w = 50 - 8 = 42$

Hence $w = \frac{42}{3} = 14$

Jul 21, 2016

$w = \frac{42}{3} = 14$

#### Explanation:

$\textcolor{m a \ge n t a}{\text{With practice you will be able to answer this question type in 1, 2 or 3 lines}}$

Gradually you manipulate the equation until you have just a single $w$ and it is on 1 side of = and everything else on the other side.

For this equation there are three basic principles that are the $\underline{\text{seed principles behind the shortcut methods}}$

$\textcolor{b r o w n}{\text{Principle 1}}$
To maintain the 'truth' of the equation (some people use the word balance): what you do to one side of the equation you do to the other.

$\textcolor{b r o w n}{\text{Principle 2}}$
To 'get rid' of an add or subtract change it to 0

$\textcolor{b r o w n}{\text{Principle 3}}$
To get rid of a multiply or divide change it to 1

Note that LHS is left hand side and that RHS is right hand side.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:$\text{ } \textcolor{b r o w n}{\frac{3 w + 8}{2} = 25}$

Using principle 3 to 'get rid' of the denominator of 2 on the LHS
Multiply both sides by $\textcolor{b l u e}{2}$

$\textcolor{b r o w n}{\frac{\textcolor{b l u e}{2}}{2} \times \left(3 w + 8\right) = \textcolor{b l u e}{2 \times} 25} \textcolor{g r e e n}{\text{ " ->" } 3 w + 8 = 50}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using principle 2 to 'get rid of the 8 on the LHS

Subtract $\textcolor{b l u e}{8}$ from both sides

color(brown)(3w+8color(blue)(-8)=50color(blue)(-8)color(green)(" "->" "3w=42)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using principle 3 to 'get rid of the 3 on the LHS

Divide both sides by $\textcolor{b l u e}{3}$ to 'get rid' of the 3 on the LHS

color(brown)(3/(color(blue)(3)) w=42/(color(blue)(3))color(green)(" "->" "w=42/3)