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Solve for $j$ . $\newline$ $|j + 1| = 7$ $\newline$ 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

|j + 1| = 7

\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 $|j + 1| = 7$ means that the expression inside the absolute value, $j + 1$ , can either be $7$ or $-7$ , because the absolute value of a number is its distance from $0$ on the number line, which is always positive.
Set up two equations: Set up two separate equations to solve for $j$ . $\newline$ Since $|j + 1|$ can be $7$ or $-7$ , we have two equations to solve: $\newline$ $1$ ) $j + 1 = 7$ $\newline$ $2$ ) $j + 1 = -7$
Solve first equation: Solve the first equation. $\newline$ Subtract $1$ from both sides of the equation $j + 1 = 7$ to isolate $j$ . $\newline$ $j + 1 - 1 = 7 - 1$ $\newline$ $j = 6$
Solve second equation: Solve the second equation. $\newline$ Subtract $1$ from both sides of the equation $j + 1 = -7$ to isolate $j$ . $\newline$ $j + 1 - 1 = -7 - 1$ $\newline$ $j = -8$

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\newline

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\newline

1

\newline

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\newline

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n=-\sqrt{3}

n=\sqrt{3}

\newline

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\$200

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\newline

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\newline

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