Question 1

What is the first step when solving the equation $$-5(3y-5)-y=-5(y-2)$$?

Accepted Answer

Apply the distributive property to both sides.

Question 2

After applying the distributive property to $$-5(3y-5)-y=-5(y-2)$$, what is the resulting equation?

Accepted Answer

$$-15y+25-y=-5y+10$$

Question 3

Which property is used to move all variable terms to one side in the equation $$-16y+25=-5y+10$$?

Accepted Answer

Addition property of equality

Question 4

What is the solution to the equation $$-5(3y-5)-y=-5(y-2)$$?

Accepted Answer

$$y=\frac{15}{11}$$

Question 5

After combining like terms in $$-15y+25-y=-5y+10$$, what is the simplified equation?

Accepted Answer

$$-16y+25=-5y+10$$

Question 6

Which step comes immediately after $$-16y+25=-5y+10 in $$solving the equation?

Accepted Answer

Add $$5y to $$both sides.

Question 7

What is the result after adding $$5y to $$both sides of $$-16y+25=-5y+10$$?

Accepted Answer

$$-11y+25=10$$

Question 8

What is the next step after $$-11y+25=10$$?

Accepted Answer

Subtract $$25$$ from both sides.

Question 9

What equation do you get after subtracting $$25$$ from both sides of $$-11y+25=10$$?

Accepted Answer

$$-11y=-15$$

Question 10

How do you solve for $$y in$$ $$-11y=-15$$?

Accepted Answer

Divide both sides by $$-11$$

Question 11

If you substitute $$y=\frac{15}{11}$$ back into the original equation $$-5(3y-5)-y=-5(y-2)$$, what should you expect?

Accepted Answer

Both sides of the equation are equal, confirming the solution.

Question 12

Which real-world scenario could be modeled by an equation similar to $$-5(3y-5)-y=-5(y-2)$$?

Accepted Answer

Calculating the net change in a bank account after multiple deposits and withdrawals.

Question 13

Which of the following is a common mistake when solving $$-5(3y-5)-y=-5(y-2)$$?

Accepted Answer

Failing to distribute $$-5$$ correctly to both terms inside the parentheses.

Question 14

If the equation $$-5(3y-5)-y=-5(y-2)$$ represented a chemical reaction, what would $$y$$ most likely represent?

Accepted Answer

The unknown quantity of a reactant needed to balance the equation.

Question 15

Which step is necessary to check your solution after solving $$-5(3y-5)-y=-5(y-2)$$?

Accepted Answer

Substitute the value of $$y$$ back into the original equation.

Solving Linear Equations Using Properties of Equality

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