Solving Linear Equations and Inequalities

The video tutorial explains how to solve a multi-step equation involving the variable t. It begins by introducing the equation and the concept of a solution. The tutorial then guides through simplifying both sides of the equation by clearing parentheses and combining like terms. Next, it demonstrates isolating the variable term using addition and subtraction, followed by solving for the variable through division. Finally, the solution is verified by substituting it back into the original equation to ensure it satisfies the equation.

What is the first step in solving the equation 3(2t - 8) = -2(t + 2)?

• Add 8 to both sides

• Distribute the numbers outside the parentheses

• Multiply both sides by 2

• Subtract 2t from both sides

After distributing, what is the expression on the left side of the equation?

• 5t - 20

• 2t - 16

• 3t - 8

• 6t - 24

What operation is used to eliminate the -2t from the right side of the equation?

• Subtract 2t from both sides

• Add 2t to both sides

• Multiply both sides by 2t

• Divide both sides by 2t

What is the result on the right side after adding 2t to both sides?

• 0

• -4

• 4

• 8

What is the next step after simplifying to 8t - 24 = 20?

• Divide both sides by 8

• Add 24 to both sides

• Subtract 24 from both sides

• Multiply both sides by 8

What is the simplified form of the fraction 20/8?

• 10/4

• 2/5

• 5/2

• 4/5

What is the final solution for t in the equation?

• t = 4/5

• t = 2/5

• t = 5

• t = 5/2

How do you verify the solution t = 5/2?

• By dividing both sides by 5/2

• By substituting t = 5/2 back into the original equation

• By multiplying both sides by 5/2

• By adding 5/2 to both sides

What is the result of substituting t = 5/2 into the left side of the original equation?

• Zero

• Negative 9

• Five

• Positive 9

What does the equation verify when both sides equal negative 9?

• The solution is incorrect

• The solution is correct

• The equation is unsolvable

• The equation needs more steps