Question

which statement is true about the equation |6x + 3| = 21?
this equation has no solution.
6x + 3 is 21 units away from zero.
6x is 21 units away from 3.
this equation has one solution.
question 5
how many solutions does the equation |9x| = -99 have? explain. select the two that apply.
there are two values of x that can be multiplied by 9 to get -99.
since we divide by zero to solve, there are no solutions.
2
there are two equations: 9x = 99 and 9x = -99.
0
an absolute value cannot equal a negative amount.

Explanation:

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First Question:

Step1: Recall absolute value definition

The absolute value $|A| = B$ (where $B>0$) means $A$ is $B$ units from 0, and has two solutions: $A=B$ or $A=-B$.

Step2: Analyze the given equation

For $|6x + 3| = 21$, this means $6x+3$ is 21 units from 0. Solving gives two solutions:
$6x+3=21 \implies 6x=18 \implies x=3$
$6x+3=-21 \implies 6x=-24 \implies x=-4$

The absolute value of any real number is non-negative (it represents a distance, which cannot be negative). The equation $|9x|=-99$ sets an absolute value equal to a negative number, which is impossible, so there are 0 solutions.

Answer:

B. $6x + 3$ is 21 units away from zero.

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Second Question: