Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 15, 2023

Solve for $k$ where $|k|-7=-6$ . Write the solution as an integer or simplified fraction.

STEP 1

Assumptions1. The absolute value of $k$ minus7 equals -6. The solution for $k$ can be an integer or a proper or improper fraction in simplest form

STEP 2

First, we need to isolate the absolute value expression on one side of the equation. We can do this by adding7 to both sides of the equation.
$|k|-7+7=-6+7$

STEP 3

implify the equation.
$|k|=1$

STEP 4

The absolute value of a number is its distance from zero on a number line, and it is always positive or zero. But it can come from a positive or a negative number. So, we can write the equation as two separate equations.
$k=1$ or $k=-1$ Both of these values for $k$ would make the original equation true because the absolute value of both1 and -1 is1.
So, the solutions are $k=1$ or $k=-1$ .

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