Writing and Simplifying Expressions
Writing and Solving Equations
Writing, Solving, and Graphing Inequalities
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

Solve and graph on number line:


-4x + 12 <= 32

-4x + 12 <= 32

-4x <= 20

x >= -5

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

What inequality is shown here:

-4<=x<3

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

Ronney wants to buy x games for his PS5 that cost 50 dollars each. He also wants to buy y games for his Xbox that cost 60 dollars each. He only has $220 to spend. Write an inequality that shows how many of each game Ronney can buy. 

x games times $50 per game plus

y games times $60 per game 

must be less than or equal to $220.

50x + 60y <=220

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

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