3. Walidate Bianca substitutes a value for $$ x $$ in the equation $$ 4 x=2 x+6 $$. a. How will Bianca know if the value is a solution of the equation?

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To determine whether a substituted value for $$ x $$ is a solution to the equation $$ 4x = 2x + 6 $$, Bianca should follow these steps:

### Step 1: Substitute the Value into the Equation
Replace $$ x $$ with the proposed value in both sides of the equation.

**For example:**
If Bianca wants to check if $$ x = 3 $$ is a solution, she would substitute 3 into the equation:

$$
4(3) = 2(3) + 6
$$

### Step 2: Simplify Both Sides of the Equation
Calculate the results of both sides after substitution.

**Continuing the example:**

$$
12 = 6 + 6
$$
$$
12 = 12
$$

### Step 3: Compare Both Sides
Check if both sides of the equation are equal after substitution.

- **If both sides are equal:** The substituted value is a **solution** to the equation.
  
  *In the example above, since $$ 12 = 12 $$, $$ x = 3 $$ is a solution.*

- **If both sides are not equal:** The substituted value is **not** a solution.

### Conclusion
Bianca knows that the substituted value is a solution to the equation $$ 4x = 2x + 6 $$ **if and only if**, after substituting the value into both sides of the equation, both sides are equal. This process verifies that the value satisfies the original equation.
To check if a value is a solution to $$ 4x = 2x + 6 $$, substitute the value for $$ x $$ in both sides. If both sides are equal, it's a solution.

3. Walidate Bianca substitutes a value for \( x \) in the equation \( 4 x=2 x+6 \). a. How will Bianca know if the value is a solution of the equation?

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