Understanding Linear Expressions and Equations

This lesson covers the concepts of equal and equivalent expressions through diagrams and comparisons. It explores expressions like x+3 and 2x, 4x and 15+x, and 2b+b and 3b, demonstrating when they are equal or not. The lesson also includes solving equations such as 80% of x equals 100 and applying these concepts to story problems.

What is the total number of units for x + 3 when x equals 1?

• 2 units

• 3 units

• 4 units

• 5 units

When x equals 3, how many units do x + 3 and 2x both equal?

• 7 units

• 8 units

• 6 units

• 5 units

For which value of x do 4x and 15 + x have the same value?

• x = 3

• x = 2

• x = 5

• x = 4

Why are 4x and 15 + x not equivalent expressions?

• They are both linear expressions.

• They are always equal.

• They are both quadratic expressions.

• They have different values for different x.

What is the value of 2b + b when b equals 2?

• 4

• 5

• 6

• 7

Are 2b + b and 3b equivalent for all values of b?

• No, they are equivalent only for b = 2.

• No, they are never equivalent.

• Yes, they are always equivalent.

• Yes, but only for b = 1.

What is the value of x when 80% of x equals 100?

• 100

• 120

• 125

• 150

How do you solve the equation 0.8x = 100 to find x?

• Multiply by 0.8

• Divide by 0.8

• Add 0.8

• Subtract 0.8

How tall is Jada's dog now if it was 5.5 inches tall as a puppy and grew 14.5 inches?

• 19 inches

• 21 inches

• 18 inches

• 20 inches

If Lynn picked 9.75 pounds of apples, which is three times the weight Andre picked, how much did Andre pick?

• 3.25 pounds

• 3.5 pounds

• 3.75 pounds

• 4 pounds