Ch 6 Review

​Ch 6 Review: Linear Equations

​Finite Math

​Solving Linear Equations

1. ​Simplify first.

2. Use inverse operations

3. Keep the equation (do the same to both sides of the equal sign).

4. When solving, do the Order of Operations in reverse.

5. Equations involving fractions, multiply through by LCD.

​Solving Linear Equations

1. ​Simplify first.

2. Use inverse operations

3. Keep the equation (do the same to both sides of the equal sign).

4. When solving, do the Order of Operations in reverse.

5. Equations involving fractions, multiply through by LCD.

Math Response

Solve.

5x + 3 - 2x = 18

Type answer here

Correct Answer: 5

Deg^°

Rad

​Solving Linear Equations

1. ​Simplify first.

2. Use inverse operations

3. Keep the equation (do the same to both sides of the equal sign).

4. When solving, do the Order of Operations in reverse.

5. Equations involving fractions, multiply through by LCD.

Math Response

Solve.

$$\frac{14}{3}x+2x=\frac{145}{6}$$

Type answer here

Correct Answer: \frac{29}{8}

Deg^°

Rad

​Solving Linear Equations

1. ​Simplify first.

2. Use inverse operations

3. Keep the equation (do the same to both sides of the equal sign).

4. When solving, do the Order of Operations in reverse.

5. Equations involving fractions, multiply through by LCD.

Math Response

Solve.

8x + 7(6 - x) = 4(2x + 7)

Type answer here

Correct Answer: 2

Deg^°

Rad

​Equations with No Solutions or All Real Numbers

​5 = -9 18 = 18

​Solving Proportions - Cross Multiply

Math Response

Solve.

$$\frac{3x-3}{7x-4}=\frac{7}{10}$$

Type answer here

Correct Answer: -\frac{2}{19}

Deg^°

Rad

Math Response

Six less than six times a number is the same as eight times the number. Find the number.

Type answer here

Correct Answer: -3

Deg^°

Rad

Math Response

It takes Jorge 48 minutes to type and spell check 9 pages of manuscript. Find how long it takes him to type and spell check 12 pages.

Type answer here

Correct Answer: 64

Deg^°

Rad

Math Response

The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 3 hours and uses 45 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 5 hours.

Type answer here

Correct Answer: 75

Deg^°

Rad

Math Response

Jason has received scores of 85, 90, and 97 on this math tests. What is the minimum score he must received on the fourth test to keep an average of at least 90%

Type answer here

Correct Answer: 88

Deg^°

Rad

Finding the Product of Polynomials

Finding the Product of Polynomials

Finding the Product of Polynomials

Finding the Product of Polynomials

Finding the Product of Polynomials

Multiple Choice

Find the product.

(5x + 1)(7x - 1)

• 21x² - 4x - 1

• 35x² + 2x - 1

• 35x² + 12x + 1

• 35x² - 12x + 1

​Factoring with the X-Method

​1. Factor out GCF (if any).
2. Identify a, b, and c.
3. ac on top and b on bottom.
4. Find candidates.
5. Divide candidates by a.
6. Write the factors.

​Factoring with the X-Method

​1. Factor out GCF (if any).
2. Identify a, b, and c.
3. ac on top and b on bottom.
4. Find candidates.
5. Divide candidates by a.
6. Write the factors.

​Factoring with the X-Method

​1. Factor out GCF (if any).
2. Identify a, b, and c.
3. ac on top and b on bottom.
4. Find candidates.
5. Divide candidates by a.
6. Write the factors.

​Factoring with the X-Method

​1. Factor out GCF (if any).
2. Identify a, b, and c.
3. ac on top and b on bottom.
4. Find candidates.
5. Divide candidates by a.
6. Write the factors.

​Factoring with the X-Method

​1. Factor out GCF (if any).
2. Identify a, b, and c.
3. ac on top and b on bottom.
4. Find candidates.
5. Divide candidates by a.
6. Write the factors.

Multiple Choice

Factor completely.

3x² + 16x - 64

• Not factorable

• (3x - 8)(x + 8)

• (3x - 8)(x - 8)

• (3x - 4)(x + 16)

Multiple Choice

Factor completely.

6x² + 72x + 120

• Not factorable

• 6(x - 10)(x - 2)

• 6(x + 10)(x + 2)

• 6(x + 5)(x + 4)

​Solving using the Zero Product Property

​1. Factor
2. Set each factor equal to zero
3. Solve.

Multiple Choice

Solve.

(2b + 7)(2b - 5) = 0

• $$\left\{-\frac{7}{2},\frac{5}{2}\right\}$$

• $$\left\{-4,\frac{5}{2}\right\}$$

• $$\left\{-2,-6\right\}$$

• $$\left\{-5,5\right\}$$

Multiple Choice

Solve.

x² + 6x + 5 = 0

• $$\left\{5\right\}$$

• $$\left\{5,1\right\}$$

• $$\left\{-5,-1\right\}$$

• $$\left\{-5,-6\right\}$$

​1. Identify a, b, c.
2. Find the discriminant, b² - 4ac
3. Finish with  

​Quadratic Formula

​What does the discriminant tell, b² - 4ac


Position >>> 2 REAL solutions

Zero >>> 1 REAL solution

Negative >>> 2 IMAGINARY solutions (no real solutions)

Multiple Choice

Solve with the quadratic formula.

3x² + 10x - 22 = 0

• No solution.

• $$\left\{-1+\sqrt[]{17},-1-\sqrt[]{17}\right\}$$

• $$\left\{\frac{-1+\sqrt[]{65}}{4},\frac{-1-\sqrt[]{65}}{4}\right\}$$

• $$\left\{\frac{-5+\sqrt[]{91}}{3},\frac{-5-\sqrt[]{91}}{3}\right\}$$

Multiple Choice

The discriminant, b² - 4ac, is equal to -5. What does this tell you about the solutions of the quadratic function?

• There are infinitely many solutions.

• There are no real solutions.

• There is 1 real solution.

• There are 2 real solutions.

Math Response

Evaluate. Use x = - 3, y = 4, and z = 5

y² - (z + x - y + z)

Type answer here

Correct Answer: 13

Deg^°

Rad

Multiple Choice

Solve.

5n - 9 > 1 - 5n

• n < -21

• {all real numbers}

• n > 1

• n > -21