Question

question 2
which equation shows an expression that is 15 units away from zero?
○ |x + 15| = 1
○ |8.5x| = 15
○ |x| + 15 = 0
○ |15x| = 0
question 3
how many solutions does the equation |x - 2| = 0 have?
○ infinitely many solutions
○ two solutions
○ no solutions
○ one solution

Explanation:

(Question 2):

Step1: Define absolute value meaning

An expression $|E|=15$ means $E$ is 15 units from 0.

Step2: Analyze each option

• $|x+15|=1$: Expression $x+15$ is 1 unit from 0.
• $|8.5x|=15$: Expression $8.5x$ is 15 units from 0.
• $|x|+15=0$: Rearranges to $|x|=-15$, impossible.
• $|15x|=0$: Expression $15x$ is 0 units from 0.

(Question 3):

Step1: Solve absolute value equation

For $|x-2|=0$, the only value making the expression inside the absolute value equal to 0 is when $x-2=0$.

Step2: Calculate the solution

$x-2=0 \implies x=2$, so there is 1 solution.

Answer:

Question 2: B. $|8.5x| = 15$
Question 3: D. One solution