Question

Solve the problems: line segment addition

Answer 1

#12

EF = 2x + 21

• DF = DE + EF
• 12 = x + 21 + 2x + 21
• 12 = 3x + 42
• 3x = 12 - 42
• 3x = -30
• x = -10

EF = 2(-10) + 21 = -20 + 21 = 1

#13

DF = x + 15

• CD = CF - DF = x + 21 - x - 15 = 6
• CD = CE - DE = x + 9 - 3 = x + 6
• x + 6 = 6
• x = 0

DF = 0 + 15 = 15

#14

BC = 2x + 26

• AD = AB + BC + CD
• 34 + x = 7 + 2x + 26 + x + 21
• 34 + x = 54 + 3x
• 3x - x = 34 - 54
• 2x = -20
• x = -10

BC = 2(-10) + 26 = -20 + 26 = 6

#15

JK = 7x - 2

• IL = IJ + JK + KL
• 2 + 7x = x + 1 + 7x - 2 + 1
• 2 + 7x = 8x
• x = 2

JK = 7(2) - 2 = 14 - 2 = 12