Question

Multiple Choice What is the value of the expression: x +|y| when x = – 3 and y = 12?

A. -15

B.-9

C. 9

D. 15

Short answer

x + |y| = 9; when x = – 3 and y = 12; Correct option: C

Step-by-step solution

Modulus Function Formula: 

Modulus Function Formula

The value of the modulus function is always non-negative. If f(x) is a modulus function, then we have:

If x ≥ 0, then f(x) = x If x = 0, then f(x) = 0 If x < 0, then f(x) = – x

This means if the value of x is greater than or equal to 0, then the modulus function takes the actual value, but if x is less than 0 then the function takes minus of the actual value 'x'.

What is absolute value and how to determine the value of variable within the absolute value. 

Absolute Value

Absolute value signs make the final result of the operations between them positive. When deciding on the order of operations, treat absolute value bars like parentheses.

|– 3| = 3: The absolute value bars make negative 3 positive.

| 3 | = 3: The absolute value bars leave positive 3 unchanged

– |– 3| = – 3: The absolute value bars make negative 3 positive. Then the negative sign takes effect, and the answer is a negative 3.

– | 3 | = – 3: The absolute value bars leave positive 3 unchanged. Then the negative sign takes effect, and the answer is a negative 3.

Step 3: Find the value of x + |y| when x = – 3 and y = 12     

We know that: | 3 | = 3: The absolute value bars leave positive 3 unchanged

According to the property,

We can find the value:$x+\left|y\right|=-3+\left|12\right|=-3+12=9$

Correct option: C