Question

the equation 4(m - 1) = 4m + 4 has no solution. how can you tell? only one side has distribution, so they dont match. when simplified, both sides have the same variable term but different constant terms. since one side has m and the other has 4m, the variable terms dont match. since one side has -1 and the other has 4, the constant terms dont match.

Explanation:

Step1: Expand the left - hand side

Use distributive property \(a(b - c)=ab - ac\). So, \(4(m - 1)=4m-4\).

Step2: Analyze the simplified equation

The original equation \(4(m - 1)=4m + 4\) becomes \(4m-4=4m + 4\). Subtract \(4m\) from both sides: \(4m-4m-4=4m-4m + 4\), which simplifies to \(-4 = 4\), a false statement. This is because when simplified, both sides have the same variable term (\(4m\)) but different constant terms (\(-4\) and \(4\)).

Answer:

When simplified, both sides have the same VARIABLE term but different CONSTANT terms.