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Solve for $j$ . $\newline$ $4 = |j + 3|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $j =$ _ or $j =$ _

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Solve absolute value equations

Full solution

Q. Solve for

j

.

\newline

4 = |j + 3|

\newline

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

\newline

j =

_____ or

j =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $4 = |j + 3|$ means that the expression inside the absolute value, $j + 3$ , can either be $4$ or $-4$ , because the absolute value of a number is always non-negative.
Set up two equations: Set up two separate equations to solve for $j$ . Since $|j + 3|$ can be $4$ or $-4$ , we have two cases: Case $1$ : $j + 3 = 4$ Case $2$ : $j + 3 = -4$
Solve first case: Solve the first case. $\newline$ For the first case, subtract $3$ from both sides to isolate $j$ : $\newline$ $j + 3 = 4$ $\newline$ $j = 4 - 3$ $\newline$ $j = 1$
Solve second case: Solve the second case. $\newline$ For the second case, subtract $3$ from both sides to isolate $j$ : $\newline$ $j + 3 = -4$ $\newline$ $j = -4 - 3$ $\newline$ $j = -7$

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\newline

What are the solutions to the given equation?

\newline

1

\newline

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\newline

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\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

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Question

\$200

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\newline

1

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