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

$\begin{gathered} |x|=d \\ \text{ then} \\ x=d\text{ or }x=-d \end{gathered}$

• If d is negative and

$\begin{gathered} |x|=-d \\ \text{then} \\ \text{ No solution, because distance (d) can not be negative.} \end{gathered}$

Therefore, the equation that has no solutions is:

$\boldsymbol{|x|=-3}$

3 0

1 year ago

Joaquin has a grade of 81 and 70 on her first two algebra test if she wants an average of 73 what possible score can she get on

Anvisha [2.4K]

81 + 70 + x = 3(73)
first multiply 3(73)

81 + 70 + x = 219
combine like terms

151 + x = 219
subtract 151 from both sides

x = 68

Joaquin needs to score a 68 on her next test to maintain an average of 73.

4 0

2 years ago