Question

Find the value of a and TV if U is between T and V
TU = 3a - 4, UV = 6a + 2, and TV = 5a + 22

Answer 1

a = 6

TV = 52

Explanation:

TU + UV = TV

3a - 4 + 6a + 2 = 5a + 22

Add like terms in RHS

3a + 6a - 4 + 2 = 5a +22

9a - 2 = 5a + 22

Add 2 to both sides

9a = 5a + 22 + 2

9a = 5a + 24

Subtract 5a from both sides

9a - 5a = 5a + 24 - 5a

4a = 24

Divide both sides by 4

4a/4 = 24/4

a = 6

TV = 5a + 22

= 5*6 + 22

= 30 + 22

TV = 52