QuestionSolve for $x$ in the equation $|x-9|=4$ . Separate your answers with a comma.

Studdy Solution

STEP 1

Assumptions1. We are solving the absolute value equation |x-9|=4. . The absolute value of a number is its distance from zero on the number line, and is always positive or zero.
3. The equation |x-9|=4 means that the distance between x and9 on the number line is4 units.

STEP 2

The absolute value equation |x-9|=4 can be rewritten as two separate equations, because the distance between x and9 can be4 units to the right or4 units to the left.
$x-9=4 \quad \text{and} \quad x-9=-4$

STEP 3

Now, we solve the first equation for x.
$x-9=$

STEP 4

Add9 to both sides of the equation to isolate x.
$x=4+9$

STEP 5

Calculate the value of x.
$x=4+9=13$

STEP 6

Next, we solve the second equation for x.
$x-9=-4$

STEP 7

Add9 to both sides of the equation to isolate x.
$x=-4+9$

STEP 8

Calculate the value of x.
$x=-4+=5$ The solutions to the equation |x-|=4 are x=13 and x=5.

Was this helpful?

QuestionSolve for $x$ in the equation $|x-9|=4$ . Separate your answers with a comma.

Studdy Solution

STEP 1

Assumptions1. We are solving the absolute value equation |x-9|=4. . The absolute value of a number is its distance from zero on the number line, and is always positive or zero.
3. The equation |x-9|=4 means that the distance between x and9 on the number line is4 units.

STEP 2

The absolute value equation |x-9|=4 can be rewritten as two separate equations, because the distance between x and9 can be4 units to the right or4 units to the left.
$x-9=4 \quad \text{and} \quad x-9=-4$

STEP 3

Now, we solve the first equation for x.
$x-9=$

STEP 4

Add9 to both sides of the equation to isolate x.
$x=4+9$

STEP 5

Calculate the value of x.
$x=4+9=13$

STEP 6

Next, we solve the second equation for x.
$x-9=-4$

STEP 7

Add9 to both sides of the equation to isolate x.
$x=-4+9$

STEP 8

Calculate the value of x.
$x=-4+=5$ The solutions to the equation |x-|=4 are x=13 and x=5.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for xxx in the equation ∣x−9∣=4|x-9|=4∣x−9∣=4. Separate your answers with a comma.

Studdy Solution

STEP 1

Assumptions1. We are solving the absolute value equation |x-9|=4. . The absolute value of a number is its distance from zero on the number line, and is always positive or zero.3. The equation |x-9|=4 means that the distance between x and9 on the number line is4 units.

STEP 2

The absolute value equation |x-9|=4 can be rewritten as two separate equations, because the distance between x and9 can be4 units to the right or4 units to the left.x−9=4andx−9=−4x-9=4 \quad \text{and} \quad x-9=-4x−9=4andx−9=−4

STEP 3

Now, we solve the first equation for x.x−9=x-9=x−9=

STEP 4

Add9 to both sides of the equation to isolate x.x=4+9x=4+9x=4+9

STEP 5

Calculate the value of x.x=4+9=13x=4+9=13x=4+9=13

STEP 6

Next, we solve the second equation for x.x−9=−4x-9=-4x−9=−4

STEP 7

Add9 to both sides of the equation to isolate x.x=−4+9x=-4+9x=−4+9

STEP 8

Calculate the value of x.x=−4+=5x=-4+=5x=−4+=5The solutions to the equation |x-|=4 are x=13 and x=5.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for $x$ in the equation $|x-9|=4$ . Separate your answers with a comma.

Assumptions1. We are solving the absolute value equation |x-9|=4. . The absolute value of a number is its distance from zero on the number line, and is always positive or zero.
3. The equation |x-9|=4 means that the distance between x and9 on the number line is4 units.

The absolute value equation |x-9|=4 can be rewritten as two separate equations, because the distance between x and9 can be4 units to the right or4 units to the left.
$x-9=4 \quad \text{and} \quad x-9=-4$

Now, we solve the first equation for x.
$x-9=$

Add9 to both sides of the equation to isolate x.
$x=4+9$

Calculate the value of x.
$x=4+9=13$

Next, we solve the second equation for x.
$x-9=-4$

Add9 to both sides of the equation to isolate x.
$x=-4+9$

Calculate the value of x.
$x=-4+=5$ The solutions to the equation |x-|=4 are x=13 and x=5.