To simplify the expression [tex]\(9.78(4.3x + 5.15)\)[/tex] using the Distributive Property, we need to distribute the [tex]\(9.78\)[/tex] across both terms inside the parenthesis.
Step 1: Distribute [tex]\(9.78\)[/tex] to the first term inside the parenthesis:
[tex]\[9.78 \times 4.3x\][/tex]
When you multiply these coefficients, you get:
[tex]\[42.054x\][/tex]
Step 2: Distribute [tex]\(9.78\)[/tex] to the second term inside the parenthesis:
[tex]\[9.78 \times 5.15\][/tex]
When you multiply these values, you get:
[tex]\[50.367\][/tex]
Step 3: Combine the results from Step 1 and Step 2 to form the simplified expression:
[tex]\[42.054x + 50.367\][/tex]
Therefore, the correct simplified form of the expression [tex]\(9.78(4.3x + 5.15)\)[/tex] is:
[tex]\[42.054x + 50.367\][/tex]
