Question

6 fill in the blank 1 point if hj = 7x - 27, find the value of x.

diagram: points h, i, j on a line segment; hi labeled 3x - 5, ij labeled x - 1

x = type your answer...

Explanation:

Step1: Analyze the segment addition

From the number line, \(HJ = HI + IJ\). So \(HJ=(3x - 5)+(x - 1)\).

Step2: Simplify the right - hand side

Simplify \((3x - 5)+(x - 1)\):
\[

$$\begin{align*} (3x - 5)+(x - 1)&=3x-5+x - 1\\ &=(3x+x)+(-5 - 1)\\ &=4x-6 \end{align*}$$

\]
We know that \(HJ = 7x-27\), so we set up the equation \(7x-27=4x - 6\).

Step3: Solve for x

Subtract \(4x\) from both sides:
\(7x-4x-27=4x-4x - 6\)
\(3x-27=-6\)
Add 27 to both sides:
\(3x-27 + 27=-6 + 27\)
\(3x=21\)
Divide both sides by 3:
\(x=\frac{21}{3}=7\)

Answer:

\(7\)