Solving Linear Equations and Inequalities for AP Precalculus

What is the main focus of Lesson 2 in the AP Pre-Calculus prerequisites review?

• Learning about polynomial functions

• Understanding trigonometric identities

• Solving linear equations and inequalities

• Graphing quadratic functions

Which step involves bringing the variables to one side and the constants to the other side?

• Bringing variables and constants to opposite sides

• Isolating the variable

• Approximating the solution

• Simplifying each side

What must you do if you multiply or divide both sides of an inequality by a negative number?

• Add the same number to both sides

• Subtract the same number from both sides

• Flip the inequality sign

• Keep the inequality sign the same

In Example 1, what is the final solution to the inequality 3x - 7 > 15x + 17?

• x > -2

• x < -2

• x > 2

• x < 2

In Example 1, why do we flip the inequality sign?

• Because we added a constant to both sides

• Because we subtracted a variable from both sides

• Because we divided both sides by a negative number

• Because we multiplied both sides by a positive number

In Example 2, what is the result after distributing -4 in the equation -4(2 + 9y) = -3(6y - 5)?

• 8 + 36y

• 8 - 36y

• -8 + 36y

• -8 - 36y

What is the simplified answer for y in Example 2?

• y = -18/23

• y = -23/18

• y = 23/18

• y = 18/23

In Example 3, what is the least common denominator used to clear the fractions?

• 3

• 2

• 4

• 6

What is the simplified equation without fractions in Example 3?

• 4x - 20 = 6x + 12

• 2x - 10 = 3x + 6

• x - 5 = 3x + 3

• 2x - 20 = 3x + 12

What is the final solution for x in Example 3?

• x = 16

• x = -16

• x = 32

• x = -32