Question

5 fill in the blank 1 point if uw = 6x - 35, find uw.
u---v (19)---w (4x - 20)
uw = type your answer...

Explanation:

Step1: Determine the relationship of segments

From the number line, \( UW = UV + VW \). We know \( UV = 19 \), \( VW = 4x - 20 \), and \( UW = 6x - 35 \). So we can set up the equation: \( 6x - 35=19+(4x - 20) \)

Step2: Solve the equation for \( x \)

Simplify the right - hand side of the equation: \( 6x - 35=19 + 4x-20=4x - 1 \)
Subtract \( 4x \) from both sides: \( 6x-4x - 35=4x - 4x-1 \), which gives \( 2x-35=-1 \)
Add 35 to both sides: \( 2x-35 + 35=-1 + 35 \), so \( 2x = 34 \)
Divide both sides by 2: \( x=\frac{34}{2}=17 \)

Step3: Find the value of \( UW \)

Substitute \( x = 17 \) into the expression for \( UW \): \( UW=6x - 35 \)
\( UW=6\times17-35=102 - 35 = 67 \)

Answer:

\( 67 \)