QuestionFind $K L$ given $K L=6 x$ , $L M=15 x-11$ , and $K M=20 x+3$ . Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The length of segment KL is $6x$ . The length of segment LM is $15x -11$
3. The length of segment KM is $20x +3$
4. The segments KL, LM, and KM form a line segment, so KL + LM = KM

STEP 2

First, we need to set up the equation based on the given information. We know that KL + LM = KM, so we can write this as $6x + (15x -11) =20x +$

STEP 3

Now, simplify the left-hand side of the equation by combining like terms.
$21x -11 =20x +3$

STEP 4

Next, we want to isolate the variable $x$ on one side of the equation. We can do this by subtracting $20x$ from both sides of the equation.
$21x -20x =11 +3$

STEP 5

implify both sides of the equation.
$x =14$

STEP 6

Now that we have the value of $x$ , we can substitute it back into the expression for KL to find the length of KL.
$KL =6x$

STEP 7

Substitute $x =14$ into the expression for KL.
$KL =6 \times14$

STEP 8

Calculate the length of KL.
$KL =6 \times14 =84$ So, the length of KL is84.

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QuestionFind $K L$ given $K L=6 x$ , $L M=15 x-11$ , and $K M=20 x+3$ . Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The length of segment KL is $6x$ . The length of segment LM is $15x -11$
3. The length of segment KM is $20x +3$
4. The segments KL, LM, and KM form a line segment, so KL + LM = KM

STEP 2

First, we need to set up the equation based on the given information. We know that KL + LM = KM, so we can write this as $6x + (15x -11) =20x +$

STEP 3

Now, simplify the left-hand side of the equation by combining like terms.
$21x -11 =20x +3$

STEP 4

Next, we want to isolate the variable $x$ on one side of the equation. We can do this by subtracting $20x$ from both sides of the equation.
$21x -20x =11 +3$

STEP 5

implify both sides of the equation.
$x =14$

STEP 6

Now that we have the value of $x$ , we can substitute it back into the expression for KL to find the length of KL.
$KL =6x$

STEP 7

Substitute $x =14$ into the expression for KL.
$KL =6 \times14$

STEP 8

Calculate the length of KL.
$KL =6 \times14 =84$ So, the length of KL is84.

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QuestionFind KLK LKL given KL=6xK L=6 xKL=6x, LM=15x−11L M=15 x-11LM=15x−11, and KM=20x+3K M=20 x+3KM=20x+3. Simplify your answer.

Studdy Solution

STEP 1

Assumptions1. The length of segment KL is 6x6x6x . The length of segment LM is 15x−1115x -1115x−113. The length of segment KM is 20x+320x +320x+34. The segments KL, LM, and KM form a line segment, so KL + LM = KM

STEP 2

First, we need to set up the equation based on the given information. We know that KL + LM = KM, so we can write this as6x+(15x−11)=20x+6x + (15x -11) =20x +6x+(15x−11)=20x+

STEP 3

Now, simplify the left-hand side of the equation by combining like terms.21x−11=20x+321x -11 =20x +321x−11=20x+3

STEP 4

Next, we want to isolate the variable xxx on one side of the equation. We can do this by subtracting 20x20x20x from both sides of the equation.21x−20x=11+321x -20x =11 +321x−20x=11+3

STEP 5

implify both sides of the equation.x=14x =14x=14

STEP 6

Now that we have the value of xxx, we can substitute it back into the expression for KL to find the length of KL.KL=6xKL =6xKL=6x

STEP 7

Substitute x=14x =14x=14 into the expression for KL.KL=6×14KL =6 \times14KL=6×14

STEP 8

Calculate the length of KL.KL=6×14=84KL =6 \times14 =84KL=6×14=84So, the length of KL is84.

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QuestionFind $K L$ given $K L=6 x$ , $L M=15 x-11$ , and $K M=20 x+3$ . Simplify your answer.

Assumptions1. The length of segment KL is $6x$ . The length of segment LM is $15x -11$
3. The length of segment KM is $20x +3$
4. The segments KL, LM, and KM form a line segment, so KL + LM = KM

First, we need to set up the equation based on the given information. We know that KL + LM = KM, so we can write this as $6x + (15x -11) =20x +$

Now, simplify the left-hand side of the equation by combining like terms.
$21x -11 =20x +3$

Next, we want to isolate the variable $x$ on one side of the equation. We can do this by subtracting $20x$ from both sides of the equation.
$21x -20x =11 +3$

implify both sides of the equation.
$x =14$

Now that we have the value of $x$ , we can substitute it back into the expression for KL to find the length of KL.
$KL =6x$

Substitute $x =14$ into the expression for KL.
$KL =6 \times14$

Calculate the length of KL.
$KL =6 \times14 =84$ So, the length of KL is84.