Mid Semester Check in

SECTION 1-3Linear & Absolute EquationsLinear & Compound InequalitiesFunctions

100

Distributive Property

3(4𝑥 + 3)

12𝑥 + 9

200

Solve for x:

3(3𝑥 + 7) = −5𝑥 + 7

x= -1

300

Find the solution set of the equation.

|3𝑥 − 8| = |5𝑥 − 6|

{−1, 7/4 } 

OR

x= -1, x= 7/4

400

Express in interval notation, and in set-builder notation. 5𝑥 − 2 < −17 𝑂𝑅 1 ≤ 4𝑥 + 1

Solution in interval notation: (−∞, −3) ∪ [0, ∞) Solution in set-builder notation: {𝑥|𝑥 < −3 or 𝑥 ≥ 0}

500

Use the graph of the function to determine the following: 

Domain: 

Range: 

𝑓(−4) = 

𝑓(1) = 

For what values of 𝑥 is 𝑓(𝑥) = 5? 

Determine the coordinates of the 𝑥- and 𝑦- intercepts. 

For what values of 𝑥 is 𝑦 negative? Express in interval notation.  

Domain: (-∞ , 5]

Range: [-3,8]

𝑓(−4) = 4

𝑓(1) = -2

For what values of 𝑥 is 𝑓(𝑥) = 5?  4

Determine the coordinates of the 𝑥- and 𝑦- intercepts. x (-2,0) and (2,0) y (0,-3)

For what values of 𝑥 is 𝑦 negative? Express in interval notation.  (-2,2)

SECTION 4-6Linear Functions and SlopesEquations of LineSystems of equations graphically

100

Calculate the slope of the line passing through the following points: (−𝟑, −𝟒) and (−𝟏, 𝟔)

m = 5 

200

Write an equation of the line that passes through the points (−2, 4) and (2, −8).

𝑦 = −3𝑥 − 2

300

Write an equation of the line that is parallel to 3𝑥 − 2𝑦 = 5 and passes through the point (6, −2).

𝑦 = 3/2 𝑥 − 11

400

Solve the following system of equations and find out if they have a solution 

2𝑥 − 3𝑦 = 6 

4𝑥 − 6𝑦 = −6

Both lines have the same slope, that is 2/3 , and different 𝑦-intercepts. This means that the lines are parallel and they will never intersect! This system of equations has no solution. We say that this system of equations is inconsistent.

500

Solve the following system of equations and find out if they have a solution

2𝑥 + 4𝑦 = 8 

𝑥 + 2𝑦 = 4

Even though we set out to graph two separate lines, we ended up with just one line! This means that the two lines actually overlap. They touch at infinitely many points. This system of equations has Infinitely many solutions. We say that this system of equations is dependent.

SECTION 7-9Systems of Equations AlgebraicallyExponentsGCF and Factoring

100

Solve the following system of equations algebraically. Check your solution. 

4𝑥 + 5𝑦 = 24 (𝐄𝐪. 𝟏) 

6𝑥 + 7𝑦 = 34 (𝐄𝐪. 𝟐)

𝑦 = 4

𝑥 = 1  

200

Solve the following system of equations algebraically.

4𝑥 + 6𝑦 = 22 (𝐄𝐪. 𝟏) 

2𝑥 + 3𝑦 = 5 (𝐄𝐪. 𝟐)

No Solution

Why?

⟹ 2𝑥 + 3𝑦 = 5 (𝐄𝐪. 𝟐) 

⟹ (−𝟐)(2𝑥) + (−𝟐)(3𝑦) = (−𝟐)(5)

⟹ −4𝑥 − 6𝑦 = −10 (𝐄𝐪. 𝟑) 

This gives us a new version of Eq. 2 which we have labeled Eq. 3. We don’t have to multiply Eq. 1 by anything. We will now add Eq. 1. to Eq. 3 

       4𝑥 + 6𝑦 = −22 (𝐄𝐪. 𝟏) 

+ − 4𝑥 − 6𝑦 = −10 (𝐄𝐪. 𝟑) 

       0!=12 

Both variables were eliminated! The bad news is we are left with a false statement since 0 does not equal 12. Therefore, there is no solution. 

300

(2 pm^-1q⁰)^-4⋅ 2m^-1p³

________________

           2pq²

    m³

_______

16p²q²

400

(8𝑥²𝑦 + 13𝑥𝑦 + 7) − (12𝑥²𝑦 − 4𝑥𝑦 + 3)

−4𝑥²𝑦 + 17𝑥𝑦 + 4

500

(12𝑥⁶𝑦³ − 16𝑥⁴𝑦² + 4𝑥𝑦) ÷ (4𝑥𝑦)

3𝑥⁵𝑦² − 4𝑥³𝑦 + 1

SECTION 10-12Factoring TrinomialsFactoring Special FormsPolynomials by factoring

100

Factor. 

5𝑥² + 13𝑥 + 6

(𝑥 + 2)(5𝑥 + 3)

200

Factor

8𝑥² − 11𝑥 + 3

(𝑥 − 1)(8𝑥 − 3)

300

Predict next 3 difference of squares:

𝑥² − 1 = (𝑥 + 1)(𝑥 − 1) 

𝑥² − 4 = (𝑥 + 2)(𝑥 − 2) 

𝑥² − 9 = (𝑥 + 3)(𝑥 − 3)

 

𝑥² − 16 = (𝑥 + 4)(𝑥 − 4) 

𝑥² − 25 = (𝑥 + 5)(𝑥 − 5) 

𝑥² − 36 = (𝑥 + 6)(𝑥 − 6)

400

Factor completely. 50𝑥² − 18𝑦²

2(5𝑥 + 3𝑦)(5𝑥 − 3𝑦)

500

Find all solutions to the equation. 

5𝑥² = 80

The solutions are 𝑥 = 4 or 𝑥 = −4

SECTION 13-15Rational FunctionsRational ExpressionsRational Equations

100

Find the domain. Express using interval notation.

𝑓(𝑥) =     3 

          ______

          𝑥² − 1

Hint: exclude values that make denominator 0.

Domain of 𝑓 = (−∞, −1) ∪ (−1, 1) ∪ (1, ∞)

200

Simplify. 

𝑥² − 4𝑥 + 3 

_________

    𝑥 − 1

= 𝑥 − 3

300

Equation on board 

  5𝑥(𝑥 + 2) 

__________

    𝑥 + 6

400

Equation on board

𝑥 = 38

500

Equation on board

x= 6