Here is the equation:
[tex]6(x-8)=72[/tex]
In the equation, 6 is being multiplied by x - 8. There are two ways to solve this equation.
FIRST METHOD
[tex]6(x-8)=72[/tex]
You need to remove the parentheses by multiplying everything in the parentheses by 6.
[tex]6(x-8) = (6\times x) + (6 \times -8)[/tex]
Multiply:
[tex]6 \times x = 6x\\6 \times -8 = -48[/tex]
Remember:
NEGATIVES
- Negative(-) times(×) negative(-) = positive(+)
- Negative(-) times(×) positive(+) = negative(-)
- Negative(-) divided(÷) by positive(+) = negative(-)
- Negative(-) divided(÷) by negative(-) = positive(+)
POSITIVES
- Positive(+) times(×) positive(+) = positive(+)
- Positive(-) times(×) negative(-) = negative(-)
- Positive(+) divided(÷) by positive(+) = positive(+)
- Positive(+) divided(÷) by negative(-) = negative(-)
Now combine the two values and rewrite the equation:
[tex]6x+-48 \rightarrow 6x-48=72[/tex]
Since you're looking for x alone, you will need to remove the -48. This can be done by adding 48 to both sides, -48+48=0, which cancels it out).
[tex]6x-48+48=72+48\\6x=120[/tex]
Lastly, divide both sides by 6 to leave x alone.
[tex]\frac{6x}{6} = \frac{120}{6}[/tex]
[tex]x=20[/tex]
SECOND METHOD
While the first step is somewhat complicated, there is a much easier way.
[tex]6(x-8)=72[/tex]
Start by dividing both sides by 6 to remove the number next to the parentheses.
[tex]\frac{6(x-8)}{6} =\frac{72}{6}[/tex]
[tex]x-8=12[/tex]
(The 6 is cancelled out since 6 divided by 6 equals 1, and 1 × any number is that number).
Now you need to leave the variable alone, which can be done by adding 8 to both sides(-8+8=0 and -8 is cancelled out).
[tex]x-8+8=12+8\\[/tex]
[tex]x=20[/tex]
Either method can be used, but the second one is definitely shorter!
The answer is x = 20.
