Question

find the value of x and st if t is between s and u, st = 7x, su = 45, and tu = 5x - 3

Explanation:

Step1: Apply segment - addition postulate

Since T is between S and U, we have $ST + TU=SU$. Substitute the given expressions: $7x+(5x - 3)=45$.

Step2: Simplify the left - hand side

Combine like terms: $7x+5x-3 = 12x-3$. So, the equation becomes $12x-3 = 45$.

Step3: Solve for x

Add 3 to both sides of the equation: $12x-3 + 3=45 + 3$, which simplifies to $12x=48$. Then divide both sides by 12: $x=\frac{48}{12}=4$.

Step4: Find the value of ST

Substitute $x = 4$ into the expression for ST. Since $ST = 7x$, then $ST=7\times4 = 28$.

Answer:

$x = 4$, $ST = 28$