Solve for k. 1 = |k − 5| Write your answers as integers or as proper or improper fractions in simplest form. k = _____ or k = _____

Understand absolute value equation: Understand the absolute value equation. The equation 1 = |k − 5| means that the expression inside the absolute value, k − 5, is either 1 or -1, because the absolute value of a number is the distance from zero, and both 1 and -1 are one unit away from zero on the number line.Set up two equations: Set up two separate equations to solve for k. Since |k − 5| can be either 1 or -1, we have two cases to consider: Case 1: k − 5 = 1 Case 2: k − 5 = -1Solve first case: Solve the first case. For the first case, k − 5 = 1, add 5 to both sides to solve for k: k − 5 + 5 = 1 + 5 k = 6Solve second case: Solve the second case. For the second case, k − 5 = -1, add 5 to both sides to solve for k: k − 5 + 5 = -1 + 5 k = 4

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Solve for $k$ . $\newline$ $1 = |k - 5|$ $\newline$ Write your answers in simplest form.

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Algebra 2

Solve absolute value equations

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Q. Solve for

k

\newline

1 = |k - 5|

\newline

Write your answers in simplest form.

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $1 = |k - 5|$ means that the expression inside the absolute value, $k - 5$ , is either $1$ or $-1$ , because the absolute value of a number is the distance from zero, and both $1$ and $-1$ are one unit away from zero on the number line.
Set up two equations: Set up two separate equations to solve for $k$ . Since $|k - 5|$ can be either $1$ or $-1$ , we have two cases to consider: Case $1$ : $k - 5 = 1$ Case $2$ : $k - 5 = -1$
Solve first case: Solve the first case. $\newline$ For the first case, $k - 5 = 1$ , add $5$ to both sides to solve for $k$ : $\newline$ $k - 5 + 5 = 1 + 5$ $\newline$ $k = 6$
Solve second case: Solve the second case. $\newline$ For the second case, $k - 5 = -1$ , add $5$ to both sides to solve for $k$ : $\newline$ $k - 5 + 5 = -1 + 5$ $\newline$ $k = 4$