Question

Question 10(Multiple Choice Worth 1 points)

Answer 1

Answer:

$x = 15$ and $x = -9$

(None of the answer choices fits. See explanation below)

Step-by-step explanation:

In mathematics, the modulus of a number, denoted by enclosing the number within vertical bars is the absolute value of the number. If the number is negative the sign is disregarded and the number is treated as positive

For example, $| -10 | = 10$ and $| 10 |$  is also $10$

Solve for $| x- 3 |$ in the equation

$\frac{1}{2} | x-3 | + 4 = 10$

Subtracting 4 on both sides yields  $\frac{1}{2} | x-3 | + 4 -4 = 10 - 4$

Simplifying $\frac{1}{2} | x-3 | = 6$

Multiplying by 2 on both sides yields $| x-3 | = 12$

We do not know if |x-3| is negative or positive since $|-12| = |12| =12$

So we have 2 possibilities

If $x - 3$  is negative, then $x - 3 = -12$ ==> $x = -9$

If $x -3$ is positive, then $x-3 = 12$  ==>  $x = 15$

So the possible values are $x = -9$ and $x = 15$

None of the answer choices fits these values indicating either an error in the answer choices or the original equation