State whether the following equations are true for the given values of the variables.
`3x=6` for `x = 3`

Answer

To determine whether the equation \(3x = 6\) is true for \(x = 3\), we will follow these steps:

### Step 1: Identify the left-hand side (LHS) of the equation
The equation given is \(3x = 6\). The left-hand side (LHS) is \(3x\).

### Step 2: Substitute the value of \(x\)
We are given that \(x = 3\). We will substitute this value into the LHS:
\[ LHS = 3 \times x = 3 \times 3 \]

### Step 3: Calculate the LHS
Now, we will perform the multiplication:
\[ LHS = 3 \times 3 = 9 \]

### Step 4: Compare LHS with the right-hand side (RHS)
The right-hand side (RHS) of the equation is \(6\). Now we will compare the LHS with the RHS:
\[ LHS = 9 \quad \text{and} \quad RHS = 6 \]

### Step 5: Determine if the equation is true
Since \(9\) (LHS) is not equal to \(6\) (RHS), we conclude that:
\[ 3x = 6 \quad \text{is not true for} \quad x = 3 \]

### Final Conclusion
Therefore, \(x = 3\) is not a solution to the equation \(3x = 6\).

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