Question

1. if hj = 7x - 27, find the value of x.

diagram: line segment with points h, i, j. hi is labeled 3x - 5, ij is labeled x - 1.
3x+
find each value.

Explanation:

Step1: Determine HJ as sum of HI and IJ

From the number line, \( HJ = HI + IJ \). Given \( HI = 3x - 5 \), \( IJ = x - 1 \), and \( HJ = 7x - 27 \), so \( 7x - 27=(3x - 5)+(x - 1) \).

Step2: Simplify the right - hand side

Simplify \( (3x - 5)+(x - 1) \): \( 3x - 5+x - 1 = 4x-6 \). So the equation becomes \( 7x - 27 = 4x-6 \).

Step3: Solve for x

Subtract \( 4x \) from both sides: \( 7x-4x - 27=4x - 4x-6 \), which gives \( 3x - 27=-6 \). Then add 27 to both sides: \( 3x-27 + 27=-6 + 27 \), so \( 3x = 21 \). Divide both sides by 3: \( x=\frac{21}{3}=7 \).

Answer:

\( x = 7 \)