Question

find the length indicated.

1. find cd

(there is a line segment with points c, d, e. the length from c to d is 2x - 3, from d to e is 3x - 4, and the total length from c to e is 18. multiple choice options: a) 9, b) 7, c) 11, d) 10)

Explanation:

Step1: Set up the equation

The total length \( CE = CD + DE \), so \( (2x - 3)+(3x - 4)=18 \).

Step2: Simplify the equation

Combine like terms: \( 2x - 3+3x - 4 = 18 \) becomes \( 5x - 7 = 18 \).

Step3: Solve for x

Add 7 to both sides: \( 5x = 18 + 7 = 25 \). Then divide by 5: \( x=\frac{25}{5}=5 \).

Step4: Find CD

Substitute \( x = 5 \) into \( CD = 2x - 3 \): \( 2(5)-3 = 10 - 3 = 7 \)? Wait, no, wait. Wait, maybe I made a mistake. Wait, let's check again. Wait, \( CD \) is \( 2x - 3 \), \( DE \) is \( 3x - 4 \), and \( CE = 18 \). So \( (2x - 3)+(3x - 4)=18 \). So \( 5x - 7 = 18 \), \( 5x = 25 \), \( x = 5 \). Then \( CD = 2(5)-3 = 10 - 3 = 7 \)? But the options are A)9, B)7, C)11, D)10. Oh, so B is 7. Wait, maybe I miscalculated. Wait, let's re - check. \( 2x - 3+3x - 4 = 18 \), \( 5x - 7 = 18 \), \( 5x = 25 \), \( x = 5 \). Then \( CD = 2*5 - 3 = 7 \). So the length of \( CD \) is 7.

Answer:

B) 7