Question

if ef = 2x - 12, fg = 3x - 15, and eg = 23, find the values of x, ef, and fg. the drawing is not to scale.

e f g (line segment diagram)

x=

ef=

fg=

Explanation:

Step1: Set up the equation

From the line segment, we know that \( EF + FG = EG \). Substituting the given expressions, we get \( (2x - 12) + (3x - 15) = 23 \).

Step2: Simplify the left side

Combine like terms: \( 2x + 3x - 12 - 15 = 23 \), which simplifies to \( 5x - 27 = 23 \).

Step3: Solve for x

Add 27 to both sides: \( 5x = 23 + 27 \), so \( 5x = 50 \). Then divide by 5: \( x = \frac{50}{5} = 10 \).

Step4: Find EF

Substitute \( x = 10 \) into \( EF = 2x - 12 \): \( EF = 2(10) - 12 = 20 - 12 = 8 \).

Step5: Find FG

Substitute \( x = 10 \) into \( FG = 3x - 15 \): \( FG = 3(10) - 15 = 30 - 15 = 15 \).

Answer:

\( x = 10 \)
\( EF = 8 \)
\( FG = 15 \)