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Solution - Linear equations with one unknown

a = 19

a=19

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Video Explanation

Watch a video of the solution to 8=1/3(a+5)

Step-by-step explanation

1. Simplify the expression

$8 = \frac{1}{3} \cdot (a + 5)$

Multiply the fraction(s):

$8 = \frac{(1 \cdot (a + 5))}{3}$

Break up the fraction:

$8 = \frac{a}{3} + \frac{5}{3}$

Swap sides:

$\frac{a}{3} + \frac{5}{3} = 8$

2. Group all constants on the right side of the equation

$\frac{a}{3} + \frac{5}{3} = 8$

Subtract $\frac{5}{3}$ from both sides:

$(\frac{a}{3} + \frac{5}{3}) - \frac{5}{3} = 8 - \frac{5}{3}$

Combine the fractions:

$\frac{a}{3} + \frac{(5 - 5)}{3} = 8 - \frac{5}{3}$

Combine the numerators:

$\frac{a}{3} + \frac{0}{3} = 8 - \frac{5}{3}$

Reduce the zero numerator:

$\frac{a}{3} + 0 = 8 - \frac{5}{3}$

Simplify the arithmetic:

$\frac{a}{3} = 8 - \frac{5}{3}$

Convert the integer into a fraction:

$\frac{a}{3} = \frac{24}{3} + \frac{- 5}{3}$

Combine the fractions:

$\frac{a}{3} = \frac{(24 - 5)}{3}$

Combine the numerators:

$\frac{a}{3} = \frac{19}{3}$

3. Isolate the a

$\frac{a}{3} = \frac{19}{3}$

Multiply both sides by $3$ :

$(\frac{a}{3}) \cdot 3 = (\frac{19}{3}) \cdot 3$

Group like terms:

$(\frac{1}{3} \cdot 3) a = (\frac{19}{3}) \cdot 3$

Multiply the coefficients:

$\frac{(1 \cdot 3)}{3} a = (\frac{19}{3}) \cdot 3$

Simplify the fraction:

$a = (\frac{19}{3}) \cdot 3$

Multiply the fraction(s):

$a = \frac{(19 \cdot 3)}{3}$

Simplify the arithmetic:

$a = 19$

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Why learn this

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

Terms and topics

Linear equations with one unknown