7. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value.\nbd = \ncd = \nbc = \nx =
7. if bd = 7x - 10, bc = 4x - 29, and cd = 5x - 9, find each value.\nbd = \ncd = \nbc = \nx =
Answer
Explanation:
Step1: Use segment - addition postulate
Since (BD=BC + CD), we substitute the given expressions: (7x - 10=(4x - 29)+(5x - 9)).
Step2: Simplify the right - hand side
Combine like terms on the right - hand side: ((4x - 29)+(5x - 9)=4x+5x-29 - 9=9x-38). So, the equation becomes (7x - 10 = 9x-38).
Step3: Solve for (x)
Subtract (7x) from both sides: (-10=9x - 7x-38), which simplifies to (-10 = 2x-38). Then add 38 to both sides: (2x=-10 + 38=28). Divide both sides by 2: (x = 14).
Step4: Find (BC)
Substitute (x = 14) into the expression for (BC): (BC=4x-29=4\times14-29=56 - 29 = 27).
Step5: Find (CD)
Substitute (x = 14) into the expression for (CD): (CD=5x-9=5\times14-9=70 - 9 = 61).
Step6: Find (BD)
Substitute (x = 14) into the expression for (BD): (BD=7x-10=7\times14-10=98 - 10 = 88).
Answer:
(x = 14) (BC = 27) (CD = 61) (BD = 88)