The absolute value measures the distance a number is away from the origin (zero) on the number line. A number can be to the left or right of zero on the number line, but the distance away from zero is always positive. Graphically:
In other words:
• If d is positive and
[tex]\begin{gathered} |x|=d \\ \text{ then} \\ x=d\text{ or }x=-d \end{gathered}[/tex]
• If d is negative and
[tex]\begin{gathered} |x|=-d \\ \text{then} \\ \text{ No solution, because distance (d) can not be negative.} \end{gathered}[/tex]
Therefore, the equation that has no solutions is:
[tex]\boldsymbol{|x|=-3}[/tex]
