QuestionFind $x$ , $K L$ , and $J L$ given that $K$ is the midpoint of $J L$ where $J L=4x-2$ and $J K=7$ .

Studdy Solution

STEP 1

Assumptions1. $K$ is the midpoint of $J$ . The length of $J$ is given by the expression $4x -$
3. The length of $JK$ is given as $7$
4. The length of a line segment is always positive

STEP 2

As $K$ is the midpoint of $J$ , the lengths of $JK$ and $KL$ are equal. Therefore, we can write $JK = KL$

STEP 3

Substitute the given value for $JK$ into the equation.
$7 = KL$

STEP 4

Since $J$ is the whole line segment, and $JK$ and $KL$ are its equal halves, we can write $J = JK + KL$

STEP 5

Substitute the given expression for $J$ and the calculated value for $KL$ into the equation.
$4x -2 =7 +7$

STEP 6

implify the right side of the equation.
$4x -2 =14$

STEP 7

To solve for $x$ , first add $2$ to both sides of the equation to isolate the term with $x$ .
$4x =14 +2$

STEP 8

implify the right side of the equation.
$4x =16$

STEP 9

Finally, divide both sides of the equation by $4$ to solve for $x$ .
$x =16 /4$

STEP 10

Calculate the value of $x$ .
$x =4$

STEP 11

Now that we have the value of $x$ , we can find the length of $J$ by substituting $x$ into the given expression for $J$ .
$J =4x -$

STEP 12

Substitute the value of $x$ into the equation.
$J =4*4 -2$

STEP 13

Calculate the value of $J$ .
$J =16 -2 =$ So, $x =$ , $KL =7$ , and $J =$ .

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QuestionFind $x$ , $K L$ , and $J L$ given that $K$ is the midpoint of $J L$ where $J L=4x-2$ and $J K=7$ .

Studdy Solution

STEP 1

Assumptions1. $K$ is the midpoint of $J$ . The length of $J$ is given by the expression $4x -$
3. The length of $JK$ is given as $7$
4. The length of a line segment is always positive

STEP 2

As $K$ is the midpoint of $J$ , the lengths of $JK$ and $KL$ are equal. Therefore, we can write $JK = KL$

STEP 3

Substitute the given value for $JK$ into the equation.
$7 = KL$

STEP 4

Since $J$ is the whole line segment, and $JK$ and $KL$ are its equal halves, we can write $J = JK + KL$

STEP 5

Substitute the given expression for $J$ and the calculated value for $KL$ into the equation.
$4x -2 =7 +7$

STEP 6

implify the right side of the equation.
$4x -2 =14$

STEP 7

To solve for $x$ , first add $2$ to both sides of the equation to isolate the term with $x$ .
$4x =14 +2$

STEP 8

implify the right side of the equation.
$4x =16$

STEP 9

Finally, divide both sides of the equation by $4$ to solve for $x$ .
$x =16 /4$

STEP 10

Calculate the value of $x$ .
$x =4$

STEP 11

Now that we have the value of $x$ , we can find the length of $J$ by substituting $x$ into the given expression for $J$ .
$J =4x -$

STEP 12

Substitute the value of $x$ into the equation.
$J =4*4 -2$

STEP 13

Calculate the value of $J$ .
$J =16 -2 =$ So, $x =$ , $KL =7$ , and $J =$ .

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QuestionFind xxx, KLK LKL, and JLJ LJL given that KKK is the midpoint of JLJ LJL where JL=4x−2J L=4x-2JL=4x−2 and JK=7J K=7JK=7.

Studdy Solution

STEP 1

Assumptions1. KKK is the midpoint of JJJ . The length of JJJ is given by the expression 4x−4x -4x−3. The length of JKJKJK is given as 7774. The length of a line segment is always positive

STEP 2

As KKK is the midpoint of JJJ, the lengths of JKJKJK and KLKLKL are equal. Therefore, we can writeJK=KLJK = KLJK=KL

STEP 3

Substitute the given value for JKJKJK into the equation.7=KL7 = KL7=KL

STEP 4

Since JJJ is the whole line segment, and JKJKJK and KLKLKL are its equal halves, we can writeJ=JK+KLJ = JK + KLJ=JK+KL

STEP 5

Substitute the given expression for JJJ and the calculated value for KLKLKL into the equation.4x−2=7+74x -2 =7 +74x−2=7+7

STEP 6

implify the right side of the equation.4x−2=144x -2 =144x−2=14

STEP 7

To solve for xxx, first add 222 to both sides of the equation to isolate the term with xxx.4x=14+24x =14 +24x=14+2

STEP 8

implify the right side of the equation.4x=164x =164x=16

STEP 9

Finally, divide both sides of the equation by 444 to solve for xxx.x=16/4x =16 /4x=16/4

STEP 10

Calculate the value of xxx.x=4x =4x=4

STEP 11

Now that we have the value of xxx, we can find the length of JJJ by substituting xxx into the given expression for JJJ.J=4x−J =4x -J=4x−

STEP 12

Substitute the value of xxx into the equation.J=4∗4−2J =4*4 -2J=4∗4−2

STEP 13

Calculate the value of JJJ.J=16−2=J =16 -2 =J=16−2=So, x=x =x=, KL=7KL =7KL=7, and J=J =J=.

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QuestionFind $x$ , $K L$ , and $J L$ given that $K$ is the midpoint of $J L$ where $J L=4x-2$ and $J K=7$ .

Assumptions1. $K$ is the midpoint of $J$ . The length of $J$ is given by the expression $4x -$
3. The length of $JK$ is given as $7$
4. The length of a line segment is always positive

As $K$ is the midpoint of $J$ , the lengths of $JK$ and $KL$ are equal. Therefore, we can write $JK = KL$

Substitute the given value for $JK$ into the equation.
$7 = KL$

Since $J$ is the whole line segment, and $JK$ and $KL$ are its equal halves, we can write $J = JK + KL$

Substitute the given expression for $J$ and the calculated value for $KL$ into the equation.
$4x -2 =7 +7$

implify the right side of the equation.
$4x -2 =14$

To solve for $x$ , first add $2$ to both sides of the equation to isolate the term with $x$ .
$4x =14 +2$

implify the right side of the equation.
$4x =16$

Finally, divide both sides of the equation by $4$ to solve for $x$ .
$x =16 /4$

Calculate the value of $x$ .
$x =4$

Now that we have the value of $x$ , we can find the length of $J$ by substituting $x$ into the given expression for $J$ .
$J =4x -$

Substitute the value of $x$ into the equation.
$J =4*4 -2$

Calculate the value of $J$ .
$J =16 -2 =$ So, $x =$ , $KL =7$ , and $J =$ .