Final answer:
To solve for x, set the expressions '3x - 4' and '5x - 16' equal to each other because they are on either side of an angle bisector, and after performing the algebra, x equals 6. Check that both expressions are equal when x = 6 to ensure the solution is correct.
Step-by-step explanation:
Solving for x Using Angle Bisector Information
When given that QS represents an angle bisector, we are told that QS divides the angle into two equal parts. Therefore, the expressions on either side of the angle bisector are equal to each other. In this case, we need to equate the expressions '3x - 4' and '5x - 16' and solve for the variable x. Let's proceed with the steps:
- Write the equation setting the two expressions equal to each other since they are bisected by QS:
3x - 4 = 5x - 16. - Solve for x by first subtracting 3x from both sides to get:
-4 = 2x - 16. - Add 16 to both sides of the equation to isolate the term with x:
12 = 2x. - Finally, divide both sides by 2 to find x:
x = 6.
After finding x, it is good practice to verify the answer by substituting it back into both expressions to ensure they are equal:
- 3(6) - 4 equals 14.
- 5(6) - 16 equals 14.
Both expressions evaluate to 14 when x = 6, confirming that our solution is correct, and the angle bisector properly divides the angle into two equal parts.