QuestionFind $B C$ given that $A C=2 x-5$ , $A B=12$ , and $B C=x-6$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment $AC$ is $x-5$ . The length of segment $AB$ is $12$
3. The length of segment $BC$ is $x-6$
4. $AC$ is the sum of $AB$ and $BC$ because they are on the same line

STEP 2

First, we need to set up an equation based on the assumption that $AC$ is the sum of $AB$ and $BC$ . $AC = AB + BC$

STEP 3

Now, plug in the given values for $AC$ , $AB$ , and $BC$ to create the equation.
$(2x-5) =12 + (x-6)$

STEP 4

implify the right side of the equation.
$(2x-) = x +6$

STEP 5

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x -5 =$

STEP 6

Add $5$ to both sides of the equation to solve for $x$ .
$x =6 +5$

STEP 7

Calculate the value of $x$ .
$x =11$

STEP 8

Now that we have the value of $x$ , we can find the length of $BC$ by substituting $x$ into the given expression for $BC$ .
$BC = x -6$

STEP 9

Plug in the value of $x$ to calculate the length of $BC$ .
$BC =11 -6$

STEP 10

Calculate the length of $BC$ .
$BC =5$ The length of $BC$ is5 units.

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QuestionFind $B C$ given that $A C=2 x-5$ , $A B=12$ , and $B C=x-6$ .

Studdy Solution

STEP 1

Assumptions1. The length of segment $AC$ is $x-5$ . The length of segment $AB$ is $12$
3. The length of segment $BC$ is $x-6$
4. $AC$ is the sum of $AB$ and $BC$ because they are on the same line

STEP 2

First, we need to set up an equation based on the assumption that $AC$ is the sum of $AB$ and $BC$ . $AC = AB + BC$

STEP 3

Now, plug in the given values for $AC$ , $AB$ , and $BC$ to create the equation.
$(2x-5) =12 + (x-6)$

STEP 4

implify the right side of the equation.
$(2x-) = x +6$

STEP 5

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x -5 =$

STEP 6

Add $5$ to both sides of the equation to solve for $x$ .
$x =6 +5$

STEP 7

Calculate the value of $x$ .
$x =11$

STEP 8

Now that we have the value of $x$ , we can find the length of $BC$ by substituting $x$ into the given expression for $BC$ .
$BC = x -6$

STEP 9

Plug in the value of $x$ to calculate the length of $BC$ .
$BC =11 -6$

STEP 10

Calculate the length of $BC$ .
$BC =5$ The length of $BC$ is5 units.

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QuestionFind BCB CBC given that AC=2x−5A C=2 x-5AC=2x−5, AB=12A B=12AB=12, and BC=x−6B C=x-6BC=x−6.

Studdy Solution

STEP 1

Assumptions1. The length of segment ACACAC is x−5x-5x−5 . The length of segment ABABAB is 1212123. The length of segment BCBCBC is x−6x-6x−64. ACACAC is the sum of ABABAB and BCBCBC because they are on the same line

STEP 2

First, we need to set up an equation based on the assumption that ACACAC is the sum of ABABAB and BCBCBC.AC=AB+BCAC = AB + BCAC=AB+BC

STEP 3

Now, plug in the given values for ACACAC, ABABAB, and BCBCBC to create the equation.(2x−5)=12+(x−6)(2x-5) =12 + (x-6)(2x−5)=12+(x−6)

STEP 4

implify the right side of the equation.(2x−)=x+6(2x-) = x +6(2x−)=x+6

STEP 5

Subtract xxx from both sides of the equation to isolate xxx on one side.x−5=x -5 =x−5=

STEP 6

Add 555 to both sides of the equation to solve for xxx.x=6+5x =6 +5x=6+5

STEP 7

Calculate the value of xxx.x=11x =11x=11

STEP 8

Now that we have the value of xxx, we can find the length of BCBCBC by substituting xxx into the given expression for BCBCBC.BC=x−6BC = x -6BC=x−6

STEP 9

Plug in the value of xxx to calculate the length of BCBCBC.BC=11−6BC =11 -6BC=11−6

STEP 10

Calculate the length of BCBCBC.BC=5BC =5BC=5The length of BCBCBC is5 units.

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QuestionFind $B C$ given that $A C=2 x-5$ , $A B=12$ , and $B C=x-6$ .

Assumptions1. The length of segment $AC$ is $x-5$ . The length of segment $AB$ is $12$
3. The length of segment $BC$ is $x-6$
4. $AC$ is the sum of $AB$ and $BC$ because they are on the same line

First, we need to set up an equation based on the assumption that $AC$ is the sum of $AB$ and $BC$ . $AC = AB + BC$

Now, plug in the given values for $AC$ , $AB$ , and $BC$ to create the equation.
$(2x-5) =12 + (x-6)$

implify the right side of the equation.
$(2x-) = x +6$

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$x -5 =$

Add $5$ to both sides of the equation to solve for $x$ .
$x =6 +5$

Calculate the value of $x$ .
$x =11$

Now that we have the value of $x$ , we can find the length of $BC$ by substituting $x$ into the given expression for $BC$ .
$BC = x -6$

Plug in the value of $x$ to calculate the length of $BC$ .
$BC =11 -6$

Calculate the length of $BC$ .
$BC =5$ The length of $BC$ is5 units.