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Solve for $z$ . $\newline$ $2 = |z - 5|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $z =$ _ or $z =$ _

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Solve absolute value equations

Full solution

Q. Solve for

z

.

\newline

2 = |z - 5|

\newline

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

\newline

z =

_____ or

z =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $2 = |z - 5|$ means that the expression inside the absolute value, $z - 5$ , is either $2$ or $-2$ , because the absolute value of a number is the distance from zero, which is always positive or zero.
Set up two equations: Set up two separate equations to solve for $z$ . Since $|z - 5|$ can be either $2$ or $-2$ , we write: $z - 5 = 2$ or $z - 5 = -2$
Solve first equation: Solve the first equation $z - 5 = 2$ . Add $5$ to both sides of the equation to isolate $z$ . $z - 5 + 5 = 2 + 5$ $z = 7$
Solve second equation: Solve the second equation $z - 5 = -2$ . Add $5$ to both sides of the equation to isolate $z$ . $z - 5 + 5 = -2 + 5$ $z = 3$

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\newline

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\newline

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Question

\$200

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\newline

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\newline

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