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Variables and Algebraic Equations
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Variables and Algebraic Equations
Use the properties of addition and multiplication to compare expressions and solve equations. Show your reasoning where asked.
Expressions and Properties
Letters can represent numbers. The order of addends or factors can change without changing their product or sum.
1.Which expression is equivalent to r + s?
- s + r
- r − s
- r × s
- r ÷ s
2.If u + v = 14, what is v + u?
- 7
- 14
- 28
- It cannot be determined
3.Select every pair of expressions that is equal for all values of the variables.
- h + k and k + h
- j − l and l − j
- a + b + c and c + a + b
- m × n and n × m
4.Match each equation to the value of the variable that must be true. Assume the same number is added to or subtracted from both sides.
- p + 6 = q + 6
- x + y = 18
- c + d + 4 = d + 11
- 3a = 3b
- x = 18 − y
- a = b
- c = 7
- p = q
Solve and Write Equations
Use equality properties to isolate the variable or write an equation that represents a situation.
5.If g + h = h + k, find g in terms of k.
6.If e + f = 23, complete the equivalent equation: f + e = .
7.Solve for x: x + 9 = 16 + 9.
8.Solve for b: a + b + c = c + 12 + a.
9.Madison has m marbles and Harper has n marbles. Write an equation showing that their total is unchanged when they swap which person has m marbles and which has n marbles.
10.Explain why 4x + 7y equals 7y + 4x for every value of x and y.
11.For the equation 2a + b = 15, write an equivalent equation that isolates b.
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