Question

1 fill in the blank 2 points
points c, h, and w are collinear. point w is between points c and h. cw = 4x - 2, hw = 5x - 19, and ch = 7x + 5.
draw a diagram to help you answer the following questions.
what is the value of x?
x = type your answer_
what is the length of $overline{hw}$?
hw = type your answer_

Explanation:

Step1: Use segment - addition postulate

Since point $W$ is between $C$ and $H$, $CW + HW=CH$. Substitute the given expressions: $(4x - 2)+(5x - 19)=7x + 5$.

Step2: Simplify the left - hand side

Combine like terms: $4x+5x-2 - 19=9x-21$. So, $9x-21 = 7x + 5$.

Step3: Solve for $x$

Subtract $7x$ from both sides: $9x-7x-21=7x-7x + 5$, which gives $2x-21 = 5$. Then add 21 to both sides: $2x-21 + 21=5 + 21$, so $2x=26$. Divide both sides by 2: $x = 13$.

Step4: Find the length of $HW$

Substitute $x = 13$ into the expression for $HW$. $HW=5x-19$. Then $HW=5\times13-19=65 - 19=46$.

Answer:

$x = 13$
$HW = 46$