Question

t, u, and v are collinear. suppose u is between t and v and that the following is true: tu = 7x - 4, uv = 6x + 10, and tv = 45. find tu.

Explanation:

Step1: Apply segment addition postulate

Since \(T\), \(U\), \(V\) are collinear and \(U\) is between \(T\) and \(V\), then \(TU + UV=TV\).
Substitute \(TU = 7x - 4\), \(UV = 6x + 10\), and \(TV = 45\) into the equation:
\((7x - 4)+(6x + 10)=45\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+6x-4 + 10=45\), which simplifies to \(13x+6 = 45\).

Step3: Solve for \(x\)

Subtract \(6\) from both sides: \(13x=45 - 6\), so \(13x=39\).
Divide both sides by \(13\): \(x=\frac{39}{13}=3\).

Step4: Find \(TU\)

Substitute \(x = 3\) into the formula for \(TU\): \(TU=7x-4\).
\(TU=7\times3-4=21 - 4=17\).

Answer:

\(17\)