Question

tape diagrams

1. here is an equation: $x + 4 = 17$

draw a tape diagram to represent the equation.

1. match each equation to one of the two tape diagrams.

a
b

______ $x + 3 = 9$
______ $9 = 3 \cdot x$
______ $3 \cdot x = 9$
______ $x = 9 - 3$
______ $3 + x = 9$
______ $x = 9 \div 3$

1. find the unknown value: $x + 5 = 21$

$x =$______

Explanation:

Step1: Solve question 1 tape diagram

The tape diagram has two parts: one labeled $x$, one labeled 4, and the total length labeled 17.

┌───────┬───┐
│   x   │ 4 │ = 17
└───────┴───┘

Step2: Match equations to diagrams

Diagram A: 3 equal parts of $x$ sum to 9. Diagram B: 2 parts, $x$ and 3, sum to 9.

• $x+3=9$ → Diagram B
• $9=3 \cdot x$ → Diagram A
• $3 \cdot x=9$ → Diagram A
• $x=9-3$ → Diagram B
• $3+x=9$ → Diagram B
• $x=9 \div 3$ → Diagram A

Step3: Solve for x in $x+5=21$

Subtract 5 from both sides.
$x = 21 - 5$

Answer:

1. Tape diagram:

┌───────┬───┐
│   x   │ 4 │ = 17
└───────┴───┘

1. Equation matches:

• $x+3=9$ → B
• $9=3 \cdot x$ → A
• $3 \cdot x=9$ → A
• $x=9-3$ → B
• $3+x=9$ → B
• $x=9 \div 3$ → A

1. $x=16$