Answer: It Equals 8
Step-by-step explanation:
Point S is on line segment \overline{RT}
RT
. Given ST=5x-7,ST=5x−7, RT=4x+9,RT=4x+9, and RS=2x+7,RS=2x+7, determine the numerical length of \overline{ST}.
ST
.
\text{Label known information:}
Label known information:
R
S
T
2x + 7
5x – 7
RT = 4x + 9
RS+ST=
RT
Segment addition postulate
\color{darkgreen}{2x+7}+\color{darkblue}{5x-7}=
2x+7+5x−7=
\,\,\color{darkred}{4x+9}
4x+9
Substitute expressions
7x=
7x=
\,\,4x+9
4x+9
Combine like terms
-4x\phantom{=}
−4x=
\,\,-4x
−4x
3x=
3x=
\,\,9
9
\frac{3x}{3}=
3
3x
=
\,\,\frac{9}{3}
3
9
Divide by 33
x=
x=
\,\,\color{darkgreen}{3}
3
\text{Plug in value of }x\text{ to find }ST\text{:}
Plug in value of x to find ST:
ST=5x-7=5\left(\color{darkgreen}{3}\right)-7=8
ST=5x−7=5(3)−7=8
\text{You can plug }x\text{ into each expression:}
You can plug x into each expression:
Optional to check work
R
S
T
2(3) + 7
5(3) – 7
RT = 4(3) + 9
\text{Simplify:}
Simplify:
R
S
T
13
8
RT = 21
\text{Final Answer:}
Final Answer:
ST=\color{green}{\mathbf{8}}
ST=8
