Writing and Simplifying Expressions
Writing and Solving Equations
Literal Equations
Linear Equations
Verifying Solutions
Linear or Non-Linear?
100
Simplify:
2x - 6 + 4x + 9
2x - 6 + 4x + 9
2x + 4x - 6 + 9
6x + 3
100
Solve:
3x - 5 = 13
3x - 5 = 13
3x = 18
x = 6
100
Evaluate this expression if A = 2, B = 4, and C = -1:
2A - B + A/C
2A - B + A/C
2(2) - (4) + (2)/(-1)
4 - 4 - 2
-2
100
Is this linear equation increasing or decreasing?
Increasing (as we go left to right, the line is moving up)
100
Is (3, -2) a solution to the equation shown here:
Yes, the point (3, -2) falls on the graph of the line and therefore it is a solution
100
Does this graph represent a linear function?
No; a linear function is one continuous line, but this is the union of two lines called |x|.
200
Simplify:
3(x - 2) - 4(2x - 5)
3(x + 2) - 4(2x - 5)
3x - 6 - 8x + 20
3x - 8x + 6 + 20
-5x + 26
200
3(x + 1) + 2x = 13
3(x + 1) + 2x = 13
3x + 3 + 2x = 13
5x + 3 = 13
5x = 10
x = 2
200
Solve this equation for A:
x + AB = C
x + AB = C
AB = C - x
A = (C - x)/B
200
Put this equation in standard form:
3y = -2x + 6
3y=-2x+6
2x+3y=6
200
Is (1, 5) a solution to the equation:
3x - y = 2
3x - y = 2
3(1) - (5) = 2
3 - 5 = 2
-2 = 2, NO
200
Is this equation a linear equation?
y + 5x^2 = 2
No, because x has an exponent of 2 it is nonlinear.
300
Jimmy bought x bags of chips for $3 each. He also bought a soda for $2.50. Write an expression that shows how much money Jimmy spent.
$3 per bag times x bags of chips plus $2.50
3x + 2.50
300
Aaliyah bought 6 apples that each weighed x pounds. She bought 4 oranges that weigh y pounds. She bought 5 grapefruit that weigh z pounds. Write an equation that gives the total weight, w, in terms of x, y, and z.
6 apples times x pounds per apple
plus 4 oranges times y pounds per orange
plus 5 grapefruit times z pounds per grapefruit
w = 6x + 4y + 5z
300
Solve this equation for A,
then evaluate if x = 2,
B = 1, and C = 5
(Ax)/C=B
(Ax)/C=B
Ax=BC
A=(BC)/x
A=((1)(5))/((2))
A = 5/2
300
Val is ordering shirts for her club. The shirts cost $12 each, and the company charges a delivery fee of $25 for every order. Write a linear equation that shows the total cost C if Val orders x shirts.
$12 per shirt times x shirts plus $25
C = 12x + 25
300
Is (4, -1) a solution to the equation:
2x = 5 - 3y
2x = 5 - 3y
2(4) = 5 -3(-1)
8 = 5 + 3
8 = 8, YES
300
Is this equation a linear equation?
4x = 5 - 3y
4x = 5 - 3y
4x + 3y = 5
Yes