Question

find the length of (overline{lo}) if m is between l and o, (lm = 7x - 9), (mo = 14) inches, and (lo = 10x - 7).

Explanation:

Step1: Use segment addition postulate

Since M is between L and O, we have \( LM + MO = LO \). Substituting the given expressions, we get \( (7x - 9) + 14 = 10x - 7 \).

Step2: Simplify and solve for x

Simplify the left side: \( 7x + 5 = 10x - 7 \). Subtract \( 7x \) from both sides: \( 5 = 3x - 7 \). Add 7 to both sides: \( 12 = 3x \). Divide by 3: \( x = 4 \).

Step3: Find length of \( \overline{LO} \)

Substitute \( x = 4 \) into \( LO = 10x - 7 \). So \( LO = 10(4) - 7 = 40 - 7 = 33 \).

Answer:

33 inches