Question

7y−4)−2(2y+2)=–32+3y. How many solutions are there?

a. No Solution
b. One Solution
c. Two Solutions
d. Infinite Solutions (All Real Numbers)

Answer 1

After simplifying and combining like terms in the equation, we arrive at a false statement, indicating that the equation has no solution.

Step-by-step explanation:

The equation given is 7y - 4 - 2(2y + 2) = –32 + 3y. To solve the equation, we will simplify and combine like terms.

1. Distribute the –2 across the (2y + 2): 7y - 4 - 4y - 4 = –32 + 3y.
2. Combine like terms on the left side: 3y - 8 = –32 + 3y.
3. Subtract 3y from both sides: –8 = –32. Notice that the y terms cancel out.
4. Add 32 to both sides to find that 24 = 0, which is a false statement.

Since we arrived at a false statement, this means that there is no solution to the equation.