Question Solve for $c$ where $-18=-9|c+2|$ . Write the solution as an integer or simplified fraction.

Studdy Solution

STEP 1

Assumptions1. The equation is $-18=-9|c+|$ . We are solving for $c$
3. The absolute value of a number is always non-negative

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the equation by $-9$ .
$|c+2| = \frac{-18}{-9}$

STEP 3

Calculate the right side of the equation.
$|c+2| =2$

STEP 4

The absolute value of a number is the distance of the number from zero on the number line. Therefore, the number can be either positive or negative. So, we can write two equations from the absolute value equation.
$c+2 =2$ or $c+2 = -2$

STEP 5

Now, solve the first equation for $c$ by subtracting $2$ from both sides.
$c =2 -2$

STEP 6

Calculate the value of $c$ from the first equation.
$c =0$

STEP 7

Now, solve the second equation for $c$ by subtracting $2$ from both sides.
$c = -2 -2$

STEP 8

Calculate the value of $c$ from the second equation.
$c = -4$ So, the solution to the equation is $c=0$ or $c=-4$ .

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Question Solve for $c$ where $-18=-9|c+2|$ . Write the solution as an integer or simplified fraction.

Studdy Solution

STEP 1

Assumptions1. The equation is $-18=-9|c+|$ . We are solving for $c$
3. The absolute value of a number is always non-negative

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the equation by $-9$ .
$|c+2| = \frac{-18}{-9}$

STEP 3

Calculate the right side of the equation.
$|c+2| =2$

STEP 4

The absolute value of a number is the distance of the number from zero on the number line. Therefore, the number can be either positive or negative. So, we can write two equations from the absolute value equation.
$c+2 =2$ or $c+2 = -2$

STEP 5

Now, solve the first equation for $c$ by subtracting $2$ from both sides.
$c =2 -2$

STEP 6

Calculate the value of $c$ from the first equation.
$c =0$

STEP 7

Now, solve the second equation for $c$ by subtracting $2$ from both sides.
$c = -2 -2$

STEP 8

Calculate the value of $c$ from the second equation.
$c = -4$ So, the solution to the equation is $c=0$ or $c=-4$ .

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Question Solve for ccc where −18=−9∣c+2∣-18=-9|c+2|−18=−9∣c+2∣. Write the solution as an integer or simplified fraction.

Studdy Solution

STEP 1

Assumptions1. The equation is −18=−9∣c+∣-18=-9|c+|−18=−9∣c+∣ . We are solving for ccc3. The absolute value of a number is always non-negative

STEP 2

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the equation by −9-9−9.∣c+2∣=−18−9|c+2| = \frac{-18}{-9}∣c+2∣=−9−18​

STEP 3

Calculate the right side of the equation.∣c+2∣=2|c+2| =2∣c+2∣=2

STEP 4

The absolute value of a number is the distance of the number from zero on the number line. Therefore, the number can be either positive or negative. So, we can write two equations from the absolute value equation.c+2=2c+2 =2c+2=2orc+2=−2c+2 = -2c+2=−2

STEP 5

Now, solve the first equation for ccc by subtracting 222 from both sides.c=2−2c =2 -2c=2−2

STEP 6

Calculate the value of ccc from the first equation.c=0c =0c=0

STEP 7

Now, solve the second equation for ccc by subtracting 222 from both sides.c=−2−2c = -2 -2c=−2−2

STEP 8

Calculate the value of ccc from the second equation.c=−4c = -4c=−4So, the solution to the equation is c=0c=0c=0 or c=−4c=-4c=−4.

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Question Solve for $c$ where $-18=-9|c+2|$ . Write the solution as an integer or simplified fraction.

Assumptions1. The equation is $-18=-9|c+|$ . We are solving for $c$
3. The absolute value of a number is always non-negative

First, we need to isolate the absolute value expression. We can do this by dividing both sides of the equation by $-9$ .
$|c+2| = \frac{-18}{-9}$

Calculate the right side of the equation.
$|c+2| =2$

The absolute value of a number is the distance of the number from zero on the number line. Therefore, the number can be either positive or negative. So, we can write two equations from the absolute value equation.
$c+2 =2$ or $c+2 = -2$

Now, solve the first equation for $c$ by subtracting $2$ from both sides.
$c =2 -2$

Calculate the value of $c$ from the first equation.
$c =0$

Now, solve the second equation for $c$ by subtracting $2$ from both sides.
$c = -2 -2$

Calculate the value of $c$ from the second equation.
$c = -4$ So, the solution to the equation is $c=0$ or $c=-4$ .