# How do you solve 1+ 3a = - 8- 4a?

Mar 25, 2018

$a = - \frac{9}{7}$

#### Explanation:

$\text{collect terms in a on the left and numeric values on the }$
$\text{right side of the equation}$

$\text{add 4a to both sides}$

$1 + 3 a + 4 a = - 8 \cancel{- 4 a} \cancel{+ 4 a}$

$\Rightarrow 1 + 7 a = - 8$

$\text{subtract 1 from both sides}$

$\cancel{1} \cancel{- 1} + 7 a = - 8 - 1$

$\Rightarrow 7 a = - 9$

$\text{divide both sides by 7}$

$\frac{\cancel{7} a}{\cancel{7}} = \frac{- 9}{7}$

$\Rightarrow a = - \frac{9}{7}$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left } = \frac{7}{7} - \frac{27}{7} = - \frac{20}{7}$

$\text{right } = - \frac{56}{7} + \frac{36}{7} = - \frac{20}{7}$

$\Rightarrow a = - \frac{9}{7} \text{ is the solution}$

Mar 25, 2018

$a = - \frac{9}{7}$

#### Explanation:

1+3a=−8−4a    Solve for $a$

1) Add $4 a$ to both sides to collect all the $a$ terms on the same side.
After you have added, you get this:
$1 + 7 a = - 8$

2) Subtract $1$ from both sides to isolate the $7 a$ term
After you subtract, you will have this:
$7 a = - 9$

3) Divide both sides by $7$ to isolate $a$
$a = - \frac{9}{7}$ $\leftarrow$ answer

$\textcolor{w h i t e}{m m m m m m m m}$―――――――――

Check
1) Sub in $- \frac{9}{7}$ in the place of $a$ in the original equation

1+3a=−8−4a

1+3(-(9)/(7)) "should equal"−8−4(-(9)/(7))

2) Clear the parentheses by distributing the coefficients

1 - (27)/(7)  "should equal" - 8 +(36)/(7)

3) To add, give the whole numbers the common denominator of $7$

(7)/(7) - (27)/(7) "should equal" - (56)/(7) +(36)/(7)

4) Add like terms

-(20)/(7)  "does equal" - (20)/(7)

$C h e c k$