Multiple Choice
Expressions may contain grouping symbols such as parentheses or brackets. To eliminate grouping symbols, you can use the ______.
A. Elimination Method
B. Distributive Property
C. Associative Property
D. Commutative Property
B. Distributive Property
What property is being applied to simplify the equation? y – 4 = 20, then y = 24
Addition property of equality
Statement 1: The expression 2(x+3) simplifies to 2x+6.
Statement 2: The solution to the equation 4x−5=11 is x=4.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
A – Statement 1 is true, and Statement 2 is true.
Solve: 0.5(s-1)=2+s
s = -5
A landlord hires a plumber to fix a burst pipe in a basement. The plumber charges a one-time service charge of $80 plus an hourly fee. The total cost the landlord had to pay the plumber for 3 hours of work was $350. Write and solve an equation to find the plumber’s hourly fee.
80 + 3h = 350; h = 90
Which of the following is NOT true when solving an equation with the variable on both sides.
A. You can isolate the variable on either the left or right side.
B. Choose the side that makes the coefficient of the variable be positive when the variable term is isolated on that side.
C. Some prefer always to isolate the variable on the left side.
D. Eliminate the variable in both sides.
D. Eliminate the variable in both sides.
Identify the property you would use to solve this equation: 6x = 60
Division property of equality
Statement 1: A literal equation is an equation in which constants have been replaced by letters.
Statement 2: A regular polygon is a polygon whose sides all have the same length and whose angles all have the same measure.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
A – Statement 1 is true, and Statement 2 is true.
Solve: 4 - x = x + 2 - 3x
x = -2
Diego is 4 years older than his brother Dan. The sum of their ages is 14. How old is Dan?
(x+4) + x = 14 ; x = 5
Which of the following is the correct step when solving for x in the equation: y = mx + b
A. Subtract b from both sides, then divide by m.
B. Add m to both sides, then subtract b.
C. Divide both sides by b, then subtract m.
D. Multiply both sides by x, then subtract y.
A. Subtract b from both sides, then divide by m.
A mathematical sentence that shows that two expressions are equivalent.
Equation
Statement 1: Terms that have the same variables and exponents.
Statement 2: The statement “Four x a number increased by five is twenty-one.” translate the mathematical equation 4x+5=21.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
B – Statement 1 is true, but Statement 2 is false.
Solve: 2/3(6m - 9) = -17 - 18m
m = -1/2
Yasmine earns $54 for dog-walking. She walks her neighbor’s dog 12 times. Write an equation to represent how to find the amount Yasmine earns per dog walk. Explain what your variable represents. How much does Yasmine earn per dog walk?
12x = 54; x= 4.5hrs
In order to isolate a variable in an equation, which operation is frequently used?
A. Addition and subtraction
B. Multiplication and division
C. Both addition and subtraction, as well as multiplication and division
D. Squaring the terms
C. Both addition and subtraction, as well as multiplication and division
Is a value of the variable that makes the equation true.
Solution of equation
Statement 1: The formula for the area of a rectangle, A=lw, can be rewritten to solve for w as w=l/A.
Statement 2: Simplifying 5x+3x−7+2 gives 8x−5.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
C – Statement 1 is false, and Statement 2 is true.
Solve: 2a -1.75a = 42.5
a = 170
Linda goes to the Lakeside Mall with friends. She spends $25 and returns home with $45. How much money d in dollars does Linda start with? Write an equation to show the amount of money Linda starts with.
d - 25 = 45; d = 70
Why might it be important to interpret the meaning of each part of an expression?
A. To ignore the smaller parts and focus only on the final result.
B. To understand the structure of the whole expression, you need to understand each of its parts.
C. To rewrite the expression randomly without following any mathematical rules.
D. To guess the solution without analyzing the components of the expression.
B. To understand the structure of the whole expression, you need to understand each of its parts.
Identify the property you would use to solve this equation: 6 + r = 16, then r = 10
Subtraction property of equality
Statement 1: The solution to 10−x=7 is x=-3
Statement 2: The expression 3(x+4) simplifies to 3x+4.
A – Statement 1 is true, and Statement 2 is true.
B – Statement 1 is true, but Statement 2 is false.
C – Statement 1 is false, and Statement 2 is true.
D – Statement 1 is false, and Statement 2 is false.
E – Cannot be determined.
D – Statement 1 is false, and Statement 2 is false.
Solve: w - 18 = w/8 - 4
w = 16
z = 3y - 2x + 2 , solve for x
x = (3y - z) / 2