Solved on Jan 23, 2024

Solve the equation $-3=-|c+4|+5$ . The solution set is

STEP 1

Assumptions
1. We are given the equation $-3=-|c+4|+5$ .
2. We need to solve for the variable $c$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

STEP 2

First, we will isolate the absolute value expression on one side of the equation by moving the constant term to the other side.
$-|c+4| = -3 - 5$

STEP 3

Now, simplify the right side of the equation.
$-|c+4| = -8$

STEP 4

Next, we will eliminate the negative sign in front of the absolute value by multiplying both sides of the equation by $-1$ .
$|c+4| = 8$

STEP 5

The absolute value equation $|c+4| = 8$ has two possible cases:
1. $c+4 = 8$
2. $c+4 = -8$
We will solve for $c$ in both cases.

STEP 6

First, let's consider the case where $c+4 = 8$ .
$c+4 = 8$

STEP 7

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = 8 - 4$

STEP 8

Now, calculate the value of $c$ .
$c = 4$

STEP 9

Next, let's consider the case where $c+4 = -8$ .
$c+4 = -8$

STEP 10

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = -8 - 4$

STEP 11

Now, calculate the value of $c$ .
$c = -12$
The solution set is $c = 4$ or $c = -12$ .

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Solve the equation $-3=-|c+4|+5$ . The solution set is

STEP 1

Assumptions
1. We are given the equation $-3=-|c+4|+5$ .
2. We need to solve for the variable $c$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

STEP 2

First, we will isolate the absolute value expression on one side of the equation by moving the constant term to the other side.
$-|c+4| = -3 - 5$

STEP 3

Now, simplify the right side of the equation.
$-|c+4| = -8$

STEP 4

Next, we will eliminate the negative sign in front of the absolute value by multiplying both sides of the equation by $-1$ .
$|c+4| = 8$

STEP 5

The absolute value equation $|c+4| = 8$ has two possible cases:
1. $c+4 = 8$
2. $c+4 = -8$
We will solve for $c$ in both cases.

STEP 6

First, let's consider the case where $c+4 = 8$ .
$c+4 = 8$

STEP 7

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = 8 - 4$

STEP 8

Now, calculate the value of $c$ .
$c = 4$

STEP 9

Next, let's consider the case where $c+4 = -8$ .
$c+4 = -8$

STEP 10

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = -8 - 4$

STEP 11

Now, calculate the value of $c$ .
$c = -12$
The solution set is $c = 4$ or $c = -12$ .

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Solve the equation −3=−∣c+4∣+5-3=-|c+4|+5−3=−∣c+4∣+5. The solution set is

STEP 1

Assumptions1. We are given the equation −3=−∣c+4∣+5-3=-|c+4|+5−3=−∣c+4∣+5.2. We need to solve for the variable ccc.3. The absolute value function ∣x∣|x|∣x∣ is defined as xxx if x≥0x \geq 0x≥0 and −x-x−x if x<0x < 0x<0.

STEP 2

First, we will isolate the absolute value expression on one side of the equation by moving the constant term to the other side.−∣c+4∣=−3−5-|c+4| = -3 - 5−∣c+4∣=−3−5

STEP 3

Now, simplify the right side of the equation.−∣c+4∣=−8-|c+4| = -8−∣c+4∣=−8

STEP 4

Next, we will eliminate the negative sign in front of the absolute value by multiplying both sides of the equation by −1-1−1.∣c+4∣=8|c+4| = 8∣c+4∣=8

STEP 5

The absolute value equation ∣c+4∣=8|c+4| = 8∣c+4∣=8 has two possible cases:1. c+4=8c+4 = 8c+4=82. c+4=−8c+4 = -8c+4=−8We will solve for ccc in both cases.

STEP 6

First, let's consider the case where c+4=8c+4 = 8c+4=8.c+4=8c+4 = 8c+4=8

STEP 7

Subtract 444 from both sides of the equation to solve for ccc.c=8−4c = 8 - 4c=8−4

STEP 8

Now, calculate the value of ccc.c=4c = 4c=4

STEP 9

Next, let's consider the case where c+4=−8c+4 = -8c+4=−8.c+4=−8c+4 = -8c+4=−8

STEP 10

Subtract 444 from both sides of the equation to solve for ccc.c=−8−4c = -8 - 4c=−8−4

STEP 11

Now, calculate the value of ccc.c=−12c = -12c=−12The solution set is c=4c = 4c=4 or c=−12c = -12c=−12.

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Solve the equation $-3=-|c+4|+5$ . The solution set is

Assumptions
1. We are given the equation $-3=-|c+4|+5$ .
2. We need to solve for the variable $c$ .
3. The absolute value function $|x|$ is defined as $x$ if $x \geq 0$ and $-x$ if $x < 0$ .

First, we will isolate the absolute value expression on one side of the equation by moving the constant term to the other side.
$-|c+4| = -3 - 5$

Now, simplify the right side of the equation.
$-|c+4| = -8$

Next, we will eliminate the negative sign in front of the absolute value by multiplying both sides of the equation by $-1$ .
$|c+4| = 8$

The absolute value equation $|c+4| = 8$ has two possible cases:
1. $c+4 = 8$
2. $c+4 = -8$
We will solve for $c$ in both cases.

First, let's consider the case where $c+4 = 8$ .
$c+4 = 8$

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = 8 - 4$

Now, calculate the value of $c$ .
$c = 4$

Next, let's consider the case where $c+4 = -8$ .
$c+4 = -8$

Subtract $4$ from both sides of the equation to solve for $c$ .
$c = -8 - 4$

Now, calculate the value of $c$ .
$c = -12$
The solution set is $c = 4$ or $c = -12$ .