QuestionSolve the equation $|1-\frac{4}{5} k|=13$ . What are the values of $k$ ? A. $\{k=-15,17.5\}$ B. $\varnothing$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is $\left|1-\frac{4}{5} k\right|=13$ .
3. We are looking for the solution set for $k$ .

STEP 2

The absolute value equation can be solved by setting up two separate equations one for the positive case and one for the negative case.
$1-\frac{4}{5}k =13$ and $1-\frac{4}{5}k = -13$

STEP 3

We can solve the first equation for $k$ by first isolating the term with $k$ .
$-\frac{}{5}k =13 -1$

STEP 4

implify the right side of the equation.
$-\frac{4}{}k =12$

STEP 5

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{12}{-\frac{4}{5}}$

STEP 6

implify the right side of the equation to find the first value of $k$ .
$k = -15$

STEP 7

Next, we solve the second equation for $k$ by first isolating the term with $k$ .
$-\frac{4}{5}k = -13 -1$

STEP 8

implify the right side of the equation.
$-\frac{4}{5}k = -14$

STEP 9

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{-14}{-\frac{4}{5}}$

STEP 10

implify the right side of the equation to find the second value of $k$ .
$k =17.5$ The solution set is $\{k=-15,17.5\}$ .

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QuestionSolve the equation $|1-\frac{4}{5} k|=13$ . What are the values of $k$ ? A. $\{k=-15,17.5\}$ B. $\varnothing$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is $\left|1-\frac{4}{5} k\right|=13$ .
3. We are looking for the solution set for $k$ .

STEP 2

The absolute value equation can be solved by setting up two separate equations one for the positive case and one for the negative case.
$1-\frac{4}{5}k =13$ and $1-\frac{4}{5}k = -13$

STEP 3

We can solve the first equation for $k$ by first isolating the term with $k$ .
$-\frac{}{5}k =13 -1$

STEP 4

implify the right side of the equation.
$-\frac{4}{}k =12$

STEP 5

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{12}{-\frac{4}{5}}$

STEP 6

implify the right side of the equation to find the first value of $k$ .
$k = -15$

STEP 7

Next, we solve the second equation for $k$ by first isolating the term with $k$ .
$-\frac{4}{5}k = -13 -1$

STEP 8

implify the right side of the equation.
$-\frac{4}{5}k = -14$

STEP 9

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{-14}{-\frac{4}{5}}$

STEP 10

implify the right side of the equation to find the second value of $k$ .
$k =17.5$ The solution set is $\{k=-15,17.5\}$ .

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QuestionSolve the equation ∣1−45k∣=13|1-\frac{4}{5} k|=13∣1−54​k∣=13. What are the values of kkk? A. {k=−15,17.5}\{k=-15,17.5\}{k=−15,17.5} B. ∅\varnothing∅.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is ∣1−45k∣=13\left|1-\frac{4}{5} k\right|=13∣∣​1−54​k∣∣​=13.3. We are looking for the solution set for kkk.

STEP 2

The absolute value equation can be solved by setting up two separate equations one for the positive case and one for the negative case.1−45k=131-\frac{4}{5}k =131−54​k=13and1−45k=−131-\frac{4}{5}k = -131−54​k=−13

STEP 3

We can solve the first equation for kkk by first isolating the term with kkk.−5k=13−1-\frac{}{5}k =13 -1−5​k=13−1

STEP 4

implify the right side of the equation.−4k=12-\frac{4}{}k =12−4​k=12

STEP 5

Next, divide both sides of the equation by −45-\frac{4}{5}−54​ to solve for kkk.k=12−45k = \frac{12}{-\frac{4}{5}}k=−54​12​

STEP 6

implify the right side of the equation to find the first value of kkk.k=−15k = -15k=−15

STEP 7

Next, we solve the second equation for kkk by first isolating the term with kkk.−45k=−13−1-\frac{4}{5}k = -13 -1−54​k=−13−1

STEP 8

implify the right side of the equation.−45k=−14-\frac{4}{5}k = -14−54​k=−14

STEP 9

Next, divide both sides of the equation by −45-\frac{4}{5}−54​ to solve for kkk.k=−14−45k = \frac{-14}{-\frac{4}{5}}k=−54​−14​

STEP 10

implify the right side of the equation to find the second value of kkk.k=17.5k =17.5k=17.5The solution set is {k=−15,17.5}\{k=-15,17.5\}{k=−15,17.5}.

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QuestionSolve the equation $|1-\frac{4}{5} k|=13$ . What are the values of $k$ ? A. $\{k=-15,17.5\}$ B. $\varnothing$ .

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative. . The equation is $\left|1-\frac{4}{5} k\right|=13$ .
3. We are looking for the solution set for $k$ .

The absolute value equation can be solved by setting up two separate equations one for the positive case and one for the negative case.
$1-\frac{4}{5}k =13$ and $1-\frac{4}{5}k = -13$

We can solve the first equation for $k$ by first isolating the term with $k$ .
$-\frac{}{5}k =13 -1$

implify the right side of the equation.
$-\frac{4}{}k =12$

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{12}{-\frac{4}{5}}$

implify the right side of the equation to find the first value of $k$ .
$k = -15$

Next, we solve the second equation for $k$ by first isolating the term with $k$ .
$-\frac{4}{5}k = -13 -1$

implify the right side of the equation.
$-\frac{4}{5}k = -14$

Next, divide both sides of the equation by $-\frac{4}{5}$ to solve for $k$ .
$k = \frac{-14}{-\frac{4}{5}}$

implify the right side of the equation to find the second value of $k$ .
$k =17.5$ The solution set is $\{k=-15,17.5\}$ .