Solved on Sep 22, 2023

Identify the graph that satisfies the absolute value equation $|x-3|=5$ .

STEP 1

Assumptions1. The absolute value equation is $|x-3|=5$ . We are looking for the graph and phrase that fits the solution to this equation

STEP 2

We need to solve the absolute value equation. An absolute value equation is an equation that contains an absolute value expression. The solution to an absolute value equation is the set of all real numbers that make the equation true.
The general form of an absolute value equation is $|a|=b$ , where $a$ is an expression and $b$ is a positive number. The solutions to this equation are $a=b$ and $a=-b$ .

STEP 3

Apply the general form of an absolute value equation to our specific equation $|x-3|=5$ . This gives us two equations to solve $x-3=5$ and $x-3=-5$ .

STEP 4

olve the first equation $x-3=$ for $x$ .
$x = +3$

STEP 5

Calculate the value of $x$ .
$x =5 +3 =8$

STEP 6

olve the second equation $x-3=-5$ for $x$ .
$x = -5 +3$

STEP 7

Calculate the value of $x$ .
$x = -5 +3 = -2$

STEP 8

The solutions to the absolute value equation $|x-3|=5$ are $x=8$ and $x=-2$ . This means that the graph of the equation includes the points where $x=8$ and $x=-2$ .

STEP 9

Compare the solutions to the options given. The correct option is the one that includes both $x=8$ and $x=-2$ .The correct answer is) Graph $(x=-2$ or $x=8)$

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Identify the graph that satisfies the absolute value equation $|x-3|=5$ .

STEP 1

Assumptions1. The absolute value equation is $|x-3|=5$ . We are looking for the graph and phrase that fits the solution to this equation

STEP 2

STEP 3

Apply the general form of an absolute value equation to our specific equation $|x-3|=5$ . This gives us two equations to solve $x-3=5$ and $x-3=-5$ .

STEP 4

olve the first equation $x-3=$ for $x$ .
$x = +3$

STEP 5

Calculate the value of $x$ .
$x =5 +3 =8$

STEP 6

olve the second equation $x-3=-5$ for $x$ .
$x = -5 +3$

STEP 7

Calculate the value of $x$ .
$x = -5 +3 = -2$

STEP 8

The solutions to the absolute value equation $|x-3|=5$ are $x=8$ and $x=-2$ . This means that the graph of the equation includes the points where $x=8$ and $x=-2$ .

STEP 9

Compare the solutions to the options given. The correct option is the one that includes both $x=8$ and $x=-2$ .The correct answer is) Graph $(x=-2$ or $x=8)$

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Identify the graph that satisfies the absolute value equation ∣x−3∣=5|x-3|=5∣x−3∣=5.

STEP 1

Assumptions1. The absolute value equation is ∣x−3∣=5|x-3|=5∣x−3∣=5 . We are looking for the graph and phrase that fits the solution to this equation

STEP 2

STEP 3

Apply the general form of an absolute value equation to our specific equation ∣x−3∣=5|x-3|=5∣x−3∣=5. This gives us two equations to solve x−3=5x-3=5x−3=5 and x−3=−5x-3=-5x−3=−5.

STEP 4

olve the first equation x−3=x-3=x−3= for xxx.x=+3x = +3x=+3

STEP 5

Calculate the value of xxx.x=5+3=8x =5 +3 =8x=5+3=8

STEP 6

olve the second equation x−3=−5x-3=-5x−3=−5 for xxx.x=−5+3x = -5 +3x=−5+3

STEP 7

Calculate the value of xxx.x=−5+3=−2x = -5 +3 = -2x=−5+3=−2

STEP 8

The solutions to the absolute value equation ∣x−3∣=5|x-3|=5∣x−3∣=5 are x=8x=8x=8 and x=−2x=-2x=−2. This means that the graph of the equation includes the points where x=8x=8x=8 and x=−2x=-2x=−2.

STEP 9

Compare the solutions to the options given. The correct option is the one that includes both x=8x=8x=8 and x=−2x=-2x=−2.The correct answer is) Graph (x=−2(x=-2(x=−2 or x=8)x=8)x=8)

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

Identify the graph that satisfies the absolute value equation $|x-3|=5$ .

Assumptions1. The absolute value equation is $|x-3|=5$ . We are looking for the graph and phrase that fits the solution to this equation

Apply the general form of an absolute value equation to our specific equation $|x-3|=5$ . This gives us two equations to solve $x-3=5$ and $x-3=-5$ .

olve the first equation $x-3=$ for $x$ .
$x = +3$

Calculate the value of $x$ .
$x =5 +3 =8$

olve the second equation $x-3=-5$ for $x$ .
$x = -5 +3$

Calculate the value of $x$ .
$x = -5 +3 = -2$

The solutions to the absolute value equation $|x-3|=5$ are $x=8$ and $x=-2$ . This means that the graph of the equation includes the points where $x=8$ and $x=-2$ .

Compare the solutions to the options given. The correct option is the one that includes both $x=8$ and $x=-2$ .The correct answer is) Graph $(x=-2$ or $x=8)$