Solve for y: 4y + 3 = 2y - 1

• A. y = 0
• B. y = -2
• C. y = 2
• D. y = 4

Answer: (B)

When solving a linear equation, the goal is to isolate the variable by using opposite operations on both sides. Start with 4y + 3 = 2y - 1. Subtract 2y from both sides to collect the y terms on one side: 2y + 3 = -1. Then subtract 3 from both sides: 2y = -4. Divide both sides by 2: y = -2. You can check by substituting back: 4(-2) + 3 = -8 + 3 = -5, and 2(-2) - 1 = -4 - 1 = -5, which matches. Choices that don’t satisfy the equation don’t balance the two sides when plugged in, so they’re not correct.