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Solve for $b$ . $\newline$ $3 = |b - 7|$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $b =$ _ or $b =$ _

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Solve absolute value equations

Full solution

Q. Solve for

b

.

\newline

3 = |b - 7|

\newline

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

\newline

b =

_____ or

b =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $3 = |b - 7|$ means that the expression inside the absolute value, $b - 7$ , is either $3$ or $-3$ , 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 $b$ . Since $|b − 7|$ can be either $3$ or $-3$ , we have two cases: Case $1$ : $b − 7 = 3$ Case $2$ : $b − 7 = -3$
Solve first case: Solve the first case. $\newline$ For the first case, $b - 7 = 3$ , add $7$ to both sides to isolate $b$ . $\newline$ $b - 7 + 7 = 3 + 7$ $\newline$ $b = 10$
Solve second case: Solve the second case. $\newline$ For the second case, $b - 7 = -3$ , add $7$ to both sides to isolate $b$ . $\newline$ $b - 7 + 7 = -3 + 7$ $\newline$ $b = 4$

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\newline

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\newline

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\newline

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