Solving Equations and Inequalities by Graphing

What is the essential question of this lesson?

• What is the importance of inequalities?

• How do you solve equations using algebra?

• What are the different types of equations?

• How can you solve an equation or inequality by graphing?

To solve the equation -3x + 20 = 5 by graphing, what should you set y equal to?

• y = 3x + 20 and y = -5

• y = 3x - 20 and y = -5

• y = -3x + 5 and y = 20

• y = -3x + 20 and y = 5

Tags

CCSS.8.EE.C.8B

What are the solutions to the equation |x - 4| = 1/2x + 1?

• x = 4 and x = 8

• x = 1 and x = 5

• x = 3 and x = 7

• x = 2 and x = 10

When solving the inequality x^2 - 4 > 0, what are the intervals where the function is positive?

• (0, ∞)

• (-2, 2)

• (-∞, 2) and (-2, ∞)

• (-∞, -2) and (2, ∞)

In the motorcycle and car problem, after how many hours will the car be ahead of the motorcycle?

• 2 hours

• 1 hour

• 3 hours

• 4 hours

To solve the inequality x + 3 > 7 - 3x, what should you graph?

• y = x - 3 and y = 7 + 3x

• y = x + 7 and y = 3 - 3x

• y = x + 3 and y = 7 - 3x

• y = x - 7 and y = 3 + 3x

Tags

CCSS.HSA.REI.D.12

What is the first step in using a table to solve the equation x^2 - 4x + 1 = x - 2?

• Sketch the graphs of y = x^2 - 4x + 1 and y = x - 2

• Find the derivative of the equation

• Solve for x algebraically

• Set y equal to zero

What is the approximate solution to the equation x^2 - 4x + 1 = x - 2 in the interval between 4 and 5?

• x ≈ 4.3

• x ≈ 4.7

• x ≈ 4.1

• x ≈ 4.9

When using graphing technology, what feature helps you find the intersection points?

• Grid feature

• Plot feature

• Zoom feature

• Intersect feature

Tags

CCSS.8.EE.C.8B

What is the summary of solving equations and inequalities by graphing?

• Graph both sides of the equation and find the intersection points.

• Solve the equation algebraically.

• Use only tables to find solutions.

• Ignore the graph and focus on the equation.