Question

find the value of x if rs = 24 centimeters. diagram: line segment rts with r to t labeled 6x - 4, t to s labeled 10 cm

Explanation:

Step1: Set up the equation

From the diagram, \( RS = RT + TS \). Given \( RT = 6x - 4 \), \( TS = 10 \), and \( RS = 24 \), so the equation is \( 6x - 4 + 10 = 24 \).

Step2: Simplify the equation

Simplify the left - hand side: \( 6x+6 = 24 \).

Step3: Solve for x

Subtract 6 from both sides: \( 6x=24 - 6=18 \). Then divide both sides by 6: \( x=\frac{18}{6} = 3 \).

Answer:

\( x = 3 \)