Final Answer:
The value of x can be found by equating PT to TQ and solving for x. In this case, 5x + 6 equals 7x - 8. By rearranging and solving, x equals 7.
Step-by-step explanation:
To find the value of x, equate the lengths of PT and TQ: 5x + 6 = 7x - 8. Begin by isolating x terms on one side: 5x - 7x = -8 - 6. Simplifying this gives us -2x = -14. To solve for x, divide both sides by -2: x = (-14) / (-2), resulting in x = 7.
Start by setting up the equation based on the given lengths PT and TQ, represented as 5x + 6 = 7x - 8. To solve for x, isolate the variable terms by moving x to one side and constants to the other. Subsequently, collect like terms to simplify the equation to -2x = -14.
Proceed with solving for x by performing the required operations. Divide both sides by the coefficient of x, which is -2. This results in x = (-14) / (-2), leading to x = 7. This step-by-step process demonstrates how to manipulate the equation to find the value of x, ensuring accuracy in the solution.
Finally, conclude by confirming that the value of x is indeed 7. Ensure each step is clear and concise, emphasizing the importance of balancing both sides of the equation to solve for the unknown variable x accurately. This explanation provides a comprehensive breakdown of the algebraic process involved in determining the value of x.