Solving Inequalities and Equations

The video tutorial covers solving equations and inequalities, focusing on isolating variables such as T, Y, H, and M. It demonstrates different strategies, including distribution, simplification, and using common denominators. The tutorial also highlights the importance of understanding the rules for solving inequalities, especially when multiplying or dividing by negative numbers.

What is the first step in solving the equation 4N = 2(T - 3) for T?

• Add 3 to both sides

• Distribute the 2

• Subtract N from both sides

• Divide both sides by 4

After distributing in the equation 4N = 2(T - 3), what is the next step to isolate T?

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the equivalent expression for T in the equation 4N = 2(T - 3) after simplification?

• T = N + 3

• T = N - 3

• T = 2N - 3

• T = 2N + 3

In the equation 6(x + 4) = 2(y + 5), what is the first step to solve for y?

• Subtract 4 from both sides

• Distribute the 6

• Divide both sides by 2

• Add 5 to both sides

What is the equivalent expression for y in the equation 6(x + 4) = 2(y + 5) after simplification?

• y = 2x - 7

• y = 2x + 7

• y = 3x + 7

• y = 3x - 7

What strategy can be used to solve the equation H/3 + H/6 = 1?

• Plug in values for H

• Multiply both sides by 6

• Subtract H from both sides

• Use a common denominator

What is the value of H that satisfies the equation H/3 + H/6 = 1?

• H = 1

• H = 2

• H = 4

• H = 3

In the distance problem, what is the equation used to find the distance M between two communities?

• M/15 - 5 = M/15 + 5

• M/10 = M/20 + 5

• M/20 = M/10 + 5

• M/15 = M/10 + 5

What is the distance M between the two communities if the equation is M/10 = M/20 + 5?

• M = 20

• M = 5

• M = 10

• M = 15

What is the first step in solving the inequality 2/3 + x/3 > 1?

• Divide both sides by 3

• Subtract 2 from both sides

• Multiply both sides by 3

• Add 1 to both sides