Question 1

Which property is used to expand $$7(7x + 9) in $$the equation $$50x + 21 = 7(7x + 9)$$?

Accepted Answer

The distributive property

Question 2

After applying the distributive property to $$7(7x + 9)$$, what is the resulting expression?

Accepted Answer

$$49x + 63$$

Question 3

What is the next step after rewriting $$50x + 21 = 49x + 63 to $$isolate $$x$$?

Accepted Answer

Subtract $$49x$$ from both sides

Question 4

Which property of equality justifies subtracting $$49x$$ from both sides of $$50x + 21 = 49x + 63$$?

Accepted Answer

Addition property of equality

Question 5

After simplifying $$50x + 21 - 49x = 49x + 63 - 49x$$, what is the resulting equation?

Accepted Answer

$$x + 21 = 63$$

Question 6

What is the solution to the equation $$x + 21 = 63$$?

Accepted Answer

$$x = 42$$

Question 7

How do you check if $$x = 42 is a $$solution to $$50x + 21 = 7(7x + 9)$$?

Accepted Answer

Substitute $$x = 42$$ into the equation and verify both sides are equal

Question 8

If $$x = 42$$, what is the value of $$50x + 21$$?

Accepted Answer

$$2,121$$

Question 9

If $$x = 42$$, what is the value of $$7(7x + 9)$$?

Accepted Answer

$$2,121$$

Question 10

Which of the following best describes the process used to solve $$50x + 21 = 7(7x + 9)$$?

Accepted Answer

Isolate the variable by applying the distributive property, then use the addition property of equality, and finally solve for $$x$$

Question 11

Suppose you encounter the equation $$ax + b = c(dx + e). $$What is the first step to solve for $$x$$?

Accepted Answer

Apply the distributive property to $$c(dx + e)$$

Question 12

Which real-world scenario could be modeled by the equation $$50x + 21 = 7(7x + 9)$$?

Accepted Answer

Calculating the total cost of $$x$$ items with a fixed fee, compared to a bulk purchase with a different pricing structure

Solving Linear Equations Using Properties of Equality

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