Question

complete the equation so it has exactly one solution.
1 + 3m + m =?
options: 4m, 4m + 1, 5m

Explanation:

Step1: Simplify Left Side

Combine like terms: \(1 + 3m + m = 1 + 4m\).

Step2: Analyze Each Option

• Option 4m: Equation becomes \(1 + 4m = 4m\). Subtract \(4m\): \(1 = 0\) (no solution).
• Option \(4m + 1\): Equation becomes \(1 + 4m = 4m + 1\). Subtract \(4m\): \(1 = 1\) (infinite solutions).
• Option 5m: Equation becomes \(1 + 4m = 5m\). Subtract \(4m\): \(1 = m\) (one solution).

Answer:

5m (the third option in the dropdown, labeled "5m")