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Solve for $d$ . $\newline$ $0 = |d + 5|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $d =$ _ or $d =$ _

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Solve absolute value equations

Full solution

Q. Solve for

d

.

\newline

0 = |d + 5|

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

d =

_____ or

d =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $0 = |d + 5|$ means that the expression inside the absolute value, $d + 5$ , can be either positive or negative, but its absolute value is $0$ . This implies that $d + 5$ itself must be $0$ .
Set up equations for d: Set up two equations to solve for d. Since the absolute value of a number is $0$ only when the number itself is $0$ , we can write two equations: $d + 5 = 0$ and $- (d + 5) = 0$ .
Solve first equation: Solve the first equation. $\newline$ $d + 5 = 0$ $\newline$ Subtract $5$ from both sides to isolate $d$ . $\newline$ $d = -5$
Solve second equation: Solve the second equation. $\newline$ $- (d + 5) = 0$ $\newline$ Multiply both sides by $-1$ to remove the negative sign. $\newline$ $d + 5 = 0$ $\newline$ Now, solve for $d$ as in Step $3$ . $\newline$ $d = -5$

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