Question

Write the expression y = 3(3y + 6) + 2y - 4 in standard form. Then, use substitution.

a. 9y + 18
b. 12y - 18
c. 11y + 22
d. 13y - 22

Answer 1

The expression y = 3(3y + 6) + 2y - 4 simplifies to -10y = 14 and then further to y = -1.4 in standard form. None of the multiple-choice options provided match this simplified expression.

Step-by-step explanation:

Transforming the Expression into Standard Form

Let's simplify the expression y = 3(3y + 6) + 2y - 4 to transform it into standard form by performing the distributive property and combining like terms:

1. Apply the distributive property: y = 3 × 3y + 3 × 6 + 2y - 4.
2. Combine like terms: y = 9y + 18 + 2y - 4. When we combine the terms with y we get 9y + 2y which is 11y. For the constant terms we have 18 - 4 which simplifies to 14.
3. Combine the coefficients of y: y = 11y + 14.
4. Subtract 11y from both sides to solve for y: y - 11y = 11y - 11y + 14, leading to -10y = 14.
5. Divide both sides by -10 to solve for y: y = -1.4.

Thus, the expression in standard form is -10y = 14, which simplifies to y = -1.4 after solving for y.

Using Substitution

Using the substitution method to solve the given expression, we would substitute the value of y we obtained into the original equation to check for correctness. However, the options provided (a-d) seem to be incorrect or unrelated to the initial problem.