QuestionFind $R S$ if $S$ is the midpoint of $\overline{R T}$ , $R S=5 x+17$ , and $S T=8 x-31$ .

Studdy Solution

STEP 1

Assumptions1. is the midpoint of line segment RT. The length of RS is given by the expression $5x +17$
3. The length of is given by the expression $8x -31$

STEP 2

Since is the midpoint of RT, the lengths of RS and are equal. We can set the expressions for RS and equal to each other and solve for x.
$RS =$

STEP 3

Substitute the given expressions for RS and into the equation.
$5x +17 =8x -31$

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Subtract $x$ from both sides of the equation.
$x -x +17 =8x -x -31$

STEP 5

implify the equation.
$17 =3x -31$

STEP 6

Next, add $31$ to both sides of the equation to isolate the term with x.
$17 +31 =3x -31 +31$

STEP 7

implify the equation.
$48 =3x$

STEP 8

Finally, divide both sides of the equation by $3$ to solve for x.
$48 /3 =3x /3$

STEP 9

implify to find the value of x.
$x =16$

STEP 10

Now that we have the value of x, we can substitute it into the expression for RS to find the length of RS.
$RS =5x +17$

STEP 11

Substitute $x =16$ into the equation.
$RS =5(16) +17$

STEP 12

Calculate the length of RS.
$RS =80 +17 =97$ So, the length of RS is97.

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QuestionFind $R S$ if $S$ is the midpoint of $\overline{R T}$ , $R S=5 x+17$ , and $S T=8 x-31$ .

Studdy Solution

STEP 1

Assumptions1. is the midpoint of line segment RT. The length of RS is given by the expression $5x +17$
3. The length of is given by the expression $8x -31$

STEP 2

Since is the midpoint of RT, the lengths of RS and are equal. We can set the expressions for RS and equal to each other and solve for x.
$RS =$

STEP 3

Substitute the given expressions for RS and into the equation.
$5x +17 =8x -31$

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Subtract $x$ from both sides of the equation.
$x -x +17 =8x -x -31$

STEP 5

implify the equation.
$17 =3x -31$

STEP 6

Next, add $31$ to both sides of the equation to isolate the term with x.
$17 +31 =3x -31 +31$

STEP 7

implify the equation.
$48 =3x$

STEP 8

Finally, divide both sides of the equation by $3$ to solve for x.
$48 /3 =3x /3$

STEP 9

implify to find the value of x.
$x =16$

STEP 10

Now that we have the value of x, we can substitute it into the expression for RS to find the length of RS.
$RS =5x +17$

STEP 11

Substitute $x =16$ into the equation.
$RS =5(16) +17$

STEP 12

Calculate the length of RS.
$RS =80 +17 =97$ So, the length of RS is97.

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QuestionFind RSR SRS if SSS is the midpoint of RT‾\overline{R T}RT, RS=5x+17R S=5 x+17RS=5x+17, and ST=8x−31S T=8 x-31ST=8x−31.

Studdy Solution

STEP 1

Assumptions1. is the midpoint of line segment RT. The length of RS is given by the expression 5x+175x +175x+173. The length of is given by the expression 8x−318x -318x−31

STEP 2

Since is the midpoint of RT, the lengths of RS and are equal. We can set the expressions for RS and equal to each other and solve for x.RS=RS =RS=

STEP 3

Substitute the given expressions for RS and into the equation.5x+17=8x−315x +17 =8x -315x+17=8x−31

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Subtract xxx from both sides of the equation.x−x+17=8x−x−31x -x +17 =8x -x -31x−x+17=8x−x−31

STEP 5

implify the equation.17=3x−3117 =3x -3117=3x−31

STEP 6

Next, add 313131 to both sides of the equation to isolate the term with x.17+31=3x−31+3117 +31 =3x -31 +3117+31=3x−31+31

STEP 7

implify the equation.48=3x48 =3x48=3x

STEP 8

Finally, divide both sides of the equation by 333 to solve for x.48/3=3x/348 /3 =3x /348/3=3x/3

STEP 9

implify to find the value of x.x=16x =16x=16

STEP 10

Now that we have the value of x, we can substitute it into the expression for RS to find the length of RS.RS=5x+17RS =5x +17RS=5x+17

STEP 11

Substitute x=16x =16x=16 into the equation.RS=5(16)+17RS =5(16) +17RS=5(16)+17

STEP 12

Calculate the length of RS.RS=80+17=97RS =80 +17 =97RS=80+17=97So, the length of RS is97.

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QuestionFind $R S$ if $S$ is the midpoint of $\overline{R T}$ , $R S=5 x+17$ , and $S T=8 x-31$ .

Assumptions1. is the midpoint of line segment RT. The length of RS is given by the expression $5x +17$
3. The length of is given by the expression $8x -31$

Since is the midpoint of RT, the lengths of RS and are equal. We can set the expressions for RS and equal to each other and solve for x.
$RS =$

Substitute the given expressions for RS and into the equation.
$5x +17 =8x -31$

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Subtract $x$ from both sides of the equation.
$x -x +17 =8x -x -31$

implify the equation.
$17 =3x -31$

Next, add $31$ to both sides of the equation to isolate the term with x.
$17 +31 =3x -31 +31$

implify the equation.
$48 =3x$

Finally, divide both sides of the equation by $3$ to solve for x.
$48 /3 =3x /3$

implify to find the value of x.
$x =16$

Now that we have the value of x, we can substitute it into the expression for RS to find the length of RS.
$RS =5x +17$

Substitute $x =16$ into the equation.
$RS =5(16) +17$

Calculate the length of RS.
$RS =80 +17 =97$ So, the length of RS is97.