IM 7.6.3 Practice: Reasoning about Equations with Tape Diagrams

Solve the equation mentally.
[math]2x=10[/math]
[math]-3x=21[/math]
[math]\frac{1}{3}x=6[/math]
[math]-\frac{1}{2}x=-7[/math]
Complete the magic squares by typing in the empty boxes so that the sum of each row, each column, and each diagonal in a grid are all equal.​
Draw a tape diagram to match the equation 5(x+1) = 20
Draw a tape diagram to match the equation 5x+1 = 20
Select [b]all[/b] the equations that match the tape diagram.[br][img]data:image/png;base64,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[/img]
The car is traveling at a constant speed. Find the number of miles the car travels in 1 hour at the given rate:
135 miles in 3 hours
22 miles in [math]\frac{1}{2}[/math] hour
7.5 miles in [math]\frac{1}{4}[/math] hour
[math]\frac{100}{3}[/math] miles in [math]\frac{2}{3}[/math] hour
[math]97\frac{1}{2}[/math] miles in [math]\frac{3}{2}[/math] hour
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Information: IM 7.6.3 Practice: Reasoning about Equations with Tape Diagrams