Question

Tonya’a first step in solving the equation .5(2y + 4)=-6 is to use the distributive property on the left side of the equation. Deon’s first step is to multiply each side by 2. Which of these methods will result in an equivalent equation? Explain

Answer 1

Both methods, using the distributive property and multiplying each side by 2, result in equivalent equations. The choice between them depends on preference, as both approaches are valid.

Both methods will result in an equivalent equation because using the distributive property and multiplying each side by 2 are essentially two different ways of expressing the same mathematical operation.

Let's demonstrate both methods:

Tonya's method (Using the Distributive Property):

`\[ 0.5(2y + 4) = -6 \]\[ 1y + 2 = -6 \]\[ y + 2 = -6 \]`

Deon's method (Multiplying each side by 2):

`\[ 2 * 0.5(2y + 4) = 2 * (-6) \]\[ 2(2y + 4) = -12 \]\[ 4y + 8 = -12 \]`

Now, let's simplify Deon's equation by subtracting 8 from both sides:

`\[ 4y + 8 - 8 = -12 - 8 \]\[ 4y = -20 \]`

Now, divide both sides by 4:

`\[ (4y)/(4) = (-20)/(4) \]\[ y = -5 \]`

So, in both cases, the solutions are the same, and both methods yield an equivalent equation. The choice between methods often depends on personal preference or simplifying the equation for easier solving.