Solving Equations and Inequalities

This video tutorial covers writing and solving multi-step equations. It explains the use of inverse operations to isolate variables and solve equations, including examples with and without parentheses. The tutorial also demonstrates solving a word problem involving the calculation of the mean. Key concepts include combining like terms, using the distributive property, and applying the reverse order of operations.

What is the primary goal when solving multi-step equations?

• To find the value of the constant

• To eliminate all coefficients

• To isolate the variable

• To simplify the equation to a single term

In the equation 3x + 15 = 24, what is the first step to isolate x?

• Divide both sides by 3

• Multiply both sides by 3

• Subtract 15 from both sides

• Add 15 to both sides

What is the inverse operation of multiplication when solving equations?

• Exponentiation

• Division

• Subtraction

• Addition

When combining like terms in the equation 8x - 6x - 25 = -35, what do you get?

• 2x + 25

• 8x - 31

• 2x - 25

• 14x - 25

In the context of solving equations, what does the term 'like terms' refer to?

• Terms with identical variable parts

• Terms with the same coefficients

• Terms that are constants

• Terms that can be factored

What is the result of simplifying 2 times the quantity (1 - 5x) + 4?

• 1 - 5x + 4

• 2 - 10x

• 2 - 5x + 4

• 2 - 10x + 4

How can you solve the equation 2(1 - 5x) + 4 = -8 without distributing?

• Add 4 to both sides, then divide by 2

• Subtract 4 from both sides, then divide by 2

• Multiply both sides by 2, then add 4

• Divide both sides by 2, then subtract 4

What is the first step in solving the equation 6 - 10x = -8?

• Divide both sides by 10

• Add 6 to both sides

• Subtract 6 from both sides

• Add 10x to both sides

What is the mean of the numbers 2, 0, 1.5, 0, and x if the mean is 1.5?

• x = 4

• x = 3

• x = 5

• x = 6

What operation should be performed first when solving 3.5 + x = 7.5?

• Add 3.5 to both sides

• Subtract 3.5 from both sides

• Divide both sides by 5

• Multiply both sides by 5