Question

consider the equation \underline{quadquad} + 5 = 3m - 4. which value or expression can you write in the blank so the equation has no solution? 0 4 3m 4m

Explanation:

Step1: Recall no - solution equation condition

For a linear equation of the form \(ax + b=cx + d\), if \(a = c\) and \(b
eq d\), the equation has no solution. Let the blank be \(x\), so the equation is \(x + 5=3m-4\), or \(x=3m - 9\). We need to find \(x\) such that when we substitute it into the original equation and simplify, we get a contradiction (like \(0m=\text{non - zero number}\)).

Step2: Test each option

• Option 0: Substitute \(x = 0\) into the equation: \(0 + 5=3m-4\), which simplifies to \(3m=9\), and \(m = 3\). This equation has a solution.
• Option 4: Substitute \(x = 4\) into the equation: \(4 + 5=3m-4\), which simplifies to \(3m=13\), and \(m=\frac{13}{3}\). This equation has a solution.
• Option \(3m\): Substitute \(x = 3m\) into the equation: \(3m+5 = 3m-4\). Subtract \(3m\) from both sides, we get \(5=-4\), which is a contradiction. So this equation has no solution.
• Option \(4m\): Substitute \(x = 4m\) into the equation: \(4m+5 = 3m-4\). Subtract \(3m\) from both sides: \(m+5=-4\), then \(m=-9\). This equation has a solution.

Answer:

\(3m\) (the option with text "3m")