To calculate: The Solution set of the equation −2=|x−3|−6.

Question

Lupe Kirkland · Accepted Answer

Calculation:
Consider the provided equation,
$- 2 = | x - 3 | - 6$
Now, add 6 to the both sides of the above equation and solve.
$- 2 = | x - 3 | - 6$
$- 2 + 6 = | x - 3 | - 6 + 6$
$4 = | x - 3 |$
According to absolute value property, two cases arise:
$4 = x - 3 or 4 = - (x - 3)$
Simplify the above expressions,
$x = 7 or x = - 1$
Check:
Substitute the value of $x = 7$ in the equation $- 2 = | x - 3 | - 6$ .
$- 2 \overset{?}{=} | 7 - 3 | - 6$
$- 2 \overset{?}{=} | 4 | - 6$
$- 2 \overset{?}{=} 4 - 6$
$- 2 \overset{?}{=} - 2$
which is true.
Now, substitute the value of $x = - 1$ in the equation $- 2 = | x - 3 | - 6$
$- 2 \overset{?}{=} | - 1 - 3 | - 6$
$- 2 \overset{?}{=} | 4 | - 6$
$- 2 \overset{?}{=} 4 - 6$
$- 2 \overset{?}{=} - 2$
which is true.
Hence, the solution set of the equation $- 2 = | x - 3 | - 6$ is (-1.7).

To calculate: The Solution set of the equation -2=|x-3|-6.

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