Vocab
What property is shown?
3(x + 2) = 3x + 6
Distributive Property
Simplify.
2x + (3x - 2) + 4
5x + 2
Solve.
6x + 3 = 15
x = 2
Solve for x.
a + x = b
x = b - a
Draw the graph of the following inequality.
x > 5
Mrs. Loganbill will check your answers.
What is the property that allows you to add the same thing to both sides of an equation?
Addition Property of Equality
Simplify.
10(x + 8) - 2 + 5x
15x + 78
Solve.
x + 18 = -2(x - 6)
x = -2
Solve for w.
xyw + z = q
w = (q - z)/xy
Solve and graph the solutions to this inequality.
2(x + 4) <= 6
x <= -1
Mrs. Loganbill will check your graphs.
What is a mathematical sentence WITHOUT an equals sign called?
Expression
Simplify.
2.5(h + 1) + 3(2h - 9)
8.5h - 24.5
Solve.
1/2(2x - 8) - 1/2(4x + 18) = 3
x = -16
The formula for the perimeter of a rectangle is P = 2l + 2w, where l is the length of the rectangle, and w is the width.
Solve for the width.
w = (P - 2l)/2
Solve the following compound inequality and graph the solutions.
-4 <= 6x - 10 < 2
-1 <= x < 2
Mrs. Loganbill will check your graphs.
What do you call an equation in which the numbers have been replaced by letters?
Literal Equation
Simplify.
1/2(x + 6) - (x + 8)
-1/2x - 5
Solve.
-(x - 1) - 5x - 29 = x - 7(x + 4)
Infinitely Many Solutions
Solve for x. State any restrictions.
a(x + b) = c
x = c/a - b OR x = (c - ba)/a
Restrictions:
a cannot be equal to zero
Solve the following compound inequality and graph the solutions.
3(x + 5) >= 4x - 7 OR 3x > -6
x <= 22 OR x > -2
Infinitely Many Solutions (entire graph shaded)
Compound Inequality
Genesis buys apples and limes at Goods Cashsaver. Apples cost $0.64 each and limes are $0.38 each. Genesis purchases a total of 25 apples and limes.
Part A: Let a be the number of apples Genesis buys. Write an expression to represent the number of limes Genesis buys.
Part B: Write an algebraic expression to represent the total cost of the apples and limes.
Part A: (25 - a)
Part B: .64a + .38(25 - a)
Solve.
1/4(x + 8) = 3/4(x - 2) + 16
x = -25
The formula to find the surface area of a cylinder is
S = 2πrh + 2πr2. Solve for h.
h = (S - 2πr2)/2πr
Solve the following compound inequality, then graph the solutions.
-1/4x > 3 AND 2(x - 1) > 0
No Solution