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?

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.