Exploring Expressions, Equations, and Inequalities

The video tutorial covers solving equations and inequalities, including using opposite operations and graphing on a number line. It provides examples and practice problems, demonstrating how to isolate variables and solve for unknowns. The tutorial also explains how to handle inequalities, especially when multiplying or dividing by negative numbers, and includes bonus problems for further practice.

What operation should you use to solve the equation 6x + 7 = 31?

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 7 from both sides

• Add 7 to both sides

When solving inequalities, what must you do if you multiply or divide by a negative number?

• Flip the inequality symbol

• Add the same number to both sides

• Keep the inequality symbol the same

• Subtract the same number from both sides

How do you represent a solution set on a number line for x < 9?

• Open dot at 9 and shade to the right

• Open dot at 9 and shade to the left

• Closed dot at 9 and shade to the right

• Closed dot at 9 and shade to the left

What does a closed dot on a number line represent?

• Greater than or equal to

• Less than

• Less than or equal to

• Greater than

What is the result of distributing -1/3 to 21x?

• 21x

• -21x

• 7x

• -7x

What is the simplified form of -7x - 5y + 8x - 16y?

• x - 21y

• -x + 21y

• x + 21y

• -x - 21y

What is the first step in solving the inequality -8x + 40 ≤ 520?

• Add 40 to both sides

• Subtract 40 from both sides

• Multiply both sides by -8

• Divide both sides by -8

If Caitlyn earns a $200 salary plus a 10% commission on book sales, what inequality represents her needing at least $350 to pay her bills?

• 200 + 0.1x ≥ 350

• 200 + 0.1x < 350

• 200 + 0.1x > 350

• 200 + 0.1x ≤ 350

What is the solution to the equation 4x - 2 = 10?

• x = 4

• x = 3

• x = 5

• x = 2

What is the solution to the inequality 1/2x - 10 > -50?

• x > -80

• x > 80

• x < -80

• x < 80