Math Problem Statement

Use the Segment Addition Postulate to find the length of ST. Given RS = 2x + 14, ST = 3x - 6, and RT = 53.

Solution

The problem asks us to use the Segment Addition Postulate to find the length of STST.

Given:

  • RS=2x+14RS = 2x + 14
  • ST=3x6ST = 3x - 6
  • RT=53RT = 53

Using the Segment Addition Postulate, we know: RS+ST=RTRS + ST = RT Substitute the given expressions: (2x+14)+(3x6)=53(2x + 14) + (3x - 6) = 53 Now solve for xx:

  1. Combine like terms: 2x+3x+146=532x + 3x + 14 - 6 = 53 5x+8=535x + 8 = 53

  2. Subtract 8 from both sides: 5x=455x = 45

  3. Divide by 5: x=9x = 9

Now that we know x=9x = 9, we can substitute it back into the expression for STST to find its length: ST=3x6=3(9)6=276=21ST = 3x - 6 = 3(9) - 6 = 27 - 6 = 21

Thus, the length of STST is 21 units.

Let me know if you want any details or explanations on any step!

Here are 5 related questions for further practice:

  1. If RS=3x+5RS = 3x + 5 and ST=2x+7ST = 2x + 7, and RT=50RT = 50, what is the value of xx?
  2. Can you derive the equation for RS+ST=RTRS + ST = RT from the diagram alone?
  3. How would the solution change if RT=45RT = 45 instead of 5353?
  4. What does the Segment Addition Postulate imply about points on a straight line?
  5. Can you verify the result by checking all segment lengths?

Tip: Always substitute the found values back into the original expressions to ensure the calculations are consistent!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Segment Addition Postulate

Formulas

RS + ST = RT

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 8-10