Question

What is the value of x in the equation below 6 (x - 8) equals 72 ​

Answer 1

Here is the equation:

$6(x-8)=72$

In the equation, 6 is being multiplied by x - 8. There are two ways to solve this equation.

FIRST METHOD

$6(x-8)=72$

You need to remove the parentheses by multiplying everything in the parentheses by 6.

$6(x-8) = (6\times x) + (6 \times -8)$

Multiply:

$6 \times x = 6x\\6 \times -8 = -48$

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:

$6x+-48 \rightarrow 6x-48=72$

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).

$6x-48+48=72+48\\6x=120$

Lastly, divide both sides by 6 to leave x alone.

$\frac{6x}{6} = \frac{120}{6}$

$x=20$

SECOND METHOD

While the first step is somewhat complicated, there is a much easier way.

$6(x-8)=72$

Start by dividing both sides by 6 to remove the number next to the parentheses.

$\frac{6(x-8)}{6} =\frac{72}{6}$

$x-8=12$

(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).

$x-8+8=12+8$

$x=20$

Either method can be used, but the second one is definitely shorter!

The answer is x = 20.

Answer 2

$\huge\blue{\tt{Given :-}}$

$\to\tt 6(x - 8) = 72$

$\huge\orange{\tt{To \: Find :-}}$

$\to\tt Value \: of \: \boxed{\bf{x}}$

$\huge\green{\tt Solution :-}$

$\tt 6 (x - 8) = 72$

$:\implies\tt 6x - 48 = 72$

$:\implies\tt 6x = 72 + 48$

$:\implies\tt 6x = 120$

$:\implies\tt x = \dfrac{\cancel{120}}{\cancel{6}}$

$:\implies\pink{\bf x = 20}$

$\huge\red{\tt Verification :-}$

We have,

• $\tt 6(x - 8) = 72$

Substituting the value of x,

$:\implies\tt 6(20 - 8) = 72$

$:\implies\tt 120 - 48 = 72$

$:\implies\tt 72 = 72$

HENCE VERIFIED