IM 6.6.8 Practice: Equal and Equivalent

Draw a diagram of x+3 and a diagram of 2x when x is 1.
Draw a diagram of x+3 and a diagram of 2x when x is 2.
Draw a diagram of x+3 and a diagram of 2x when x is 3.
Draw a diagram of x+3 and a diagram of 2x when x is 4.
When are [math]x+3[/math] and [math]2x[/math] equal? When are they not equal? Use your diagrams to explain.
Do [math]4x[/math] and [math]15+x[/math] have the same value when [math]x[/math] is 5?
Are [math]4x[/math] and [math]15+x[/math] equivalent expressions? Explain your reasoning.
Check that [math]2b+b[/math] and [math]3b[/math] have the same value when [math]b[/math] is 1.
Check that [math]2b+b[/math] and [math]3b[/math] have the same value when [math]b[/math] is 2.
Check that [math]2b+b[/math] and [math]3b[/math] have the same value when [math]b[/math] is 3.
Do [math]2b+b[/math] and [math]3b[/math] have the same value for all values of [math]b[/math]? Explain your reasoning.
Are [math]2b+b[/math] and [math]3b[/math] equivalent expressions?
80% of x is equal to 100.
Write an equation that shows the relationship of 80%, [math]x[/math], and 100.
Use your equation to find [math]x[/math].[br][br]
For each story problem, write an equation to represent the problem and then solve the equation. Be sure to explain the meaning of any variables you use.
Jada’s dog was [math]5\frac{1}{2}[/math] inches tall when it was a puppy. Now her dog is [math]14\frac{1}{2}[/math] inches taller than that. How tall is Jada’s dog now?
Lin picked [math]9\frac{3}{4}[/math] pounds of apples, which was 3 times the weight of the apples Andre picked. How many pounds of apples did Andre pick?
Find these products.
[math](2.3)\cdot(1.4)[/math]
[math](1.72)\cdot(2.6)[/math]
[math](18.2)\cdot(0.2)[/math]
[math]15\cdot(1.2)[/math]
Calculate [math]141.75\div2.5[/math] using a method of your choice. Show or explain your reasoning.
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Information: IM 6.6.8 Practice: Equal and Equivalent