QuestionSolve the equation $8|x-3|=88$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|x|$ can be either $x$ or $-x$ . . We are solving for $x$ in the equation $8|x-3|=88$ .

STEP 2

First, we need to isolate the absolute value by dividing both sides of the equation by8.
$|x-| = \frac{88}{8}$

STEP 3

Now, calculate the right side of the equation.
$|x-3| =11$

STEP 4

Next, we can create two equations to solve for $x$ , because the absolute value of a number can be either positive or negative.
$x-3 =11$ $x-3 = -11$

STEP 5

Now, solve the first equation for $x$ .
$x =11 +3$

STEP 6

Calculate the value of $x$ from the first equation.
$x =14$

STEP 7

Next, solve the second equation for $x$ .
$x = -11 +3$

STEP 8

Calculate the value of $x$ from the second equation.
$x = -8$ So, the solutions to the equation $8|x-3|=88$ are $x =14$ and $x = -8$ .

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QuestionSolve the equation $8|x-3|=88$ .

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|x|$ can be either $x$ or $-x$ . . We are solving for $x$ in the equation $8|x-3|=88$ .

STEP 2

First, we need to isolate the absolute value by dividing both sides of the equation by8.
$|x-| = \frac{88}{8}$

STEP 3

Now, calculate the right side of the equation.
$|x-3| =11$

STEP 4

Next, we can create two equations to solve for $x$ , because the absolute value of a number can be either positive or negative.
$x-3 =11$ $x-3 = -11$

STEP 5

Now, solve the first equation for $x$ .
$x =11 +3$

STEP 6

Calculate the value of $x$ from the first equation.
$x =14$

STEP 7

Next, solve the second equation for $x$ .
$x = -11 +3$

STEP 8

Calculate the value of $x$ from the second equation.
$x = -8$ So, the solutions to the equation $8|x-3|=88$ are $x =14$ and $x = -8$ .

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QuestionSolve the equation 8∣x−3∣=888|x-3|=888∣x−3∣=88.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, ∣x∣|x|∣x∣ can be either xxx or −x-x−x. . We are solving for xxx in the equation 8∣x−3∣=888|x-3|=888∣x−3∣=88.

STEP 2

First, we need to isolate the absolute value by dividing both sides of the equation by8.∣x−∣=888|x-| = \frac{88}{8}∣x−∣=888​

STEP 3

Now, calculate the right side of the equation.∣x−3∣=11|x-3| =11∣x−3∣=11

STEP 4

Next, we can create two equations to solve for xxx, because the absolute value of a number can be either positive or negative.x−3=11x-3 =11x−3=11x−3=−11x-3 = -11x−3=−11

STEP 5

Now, solve the first equation for xxx.x=11+3x =11 +3x=11+3

STEP 6

Calculate the value of xxx from the first equation.x=14x =14x=14

STEP 7

Next, solve the second equation for xxx.x=−11+3x = -11 +3x=−11+3

STEP 8

Calculate the value of xxx from the second equation.x=−8x = -8x=−8So, the solutions to the equation 8∣x−3∣=888|x-3|=888∣x−3∣=88 are x=14x =14x=14 and x=−8x = -8x=−8.

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QuestionSolve the equation $8|x-3|=88$ .

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|x|$ can be either $x$ or $-x$ . . We are solving for $x$ in the equation $8|x-3|=88$ .

First, we need to isolate the absolute value by dividing both sides of the equation by8.
$|x-| = \frac{88}{8}$

Now, calculate the right side of the equation.
$|x-3| =11$

Next, we can create two equations to solve for $x$ , because the absolute value of a number can be either positive or negative.
$x-3 =11$ $x-3 = -11$

Now, solve the first equation for $x$ .
$x =11 +3$

Calculate the value of $x$ from the first equation.
$x =14$

Next, solve the second equation for $x$ .
$x = -11 +3$

Calculate the value of $x$ from the second equation.
$x = -8$ So, the solutions to the equation $8|x-3|=88$ are $x =14$ and $x = -8$ .