Question

Which equations are equivalent to −4(3d−2)−7?

A) −12d−15

B) 12d−15

C) None of the above

Answer 1

After distributing −4 across the original expression −4(3d−2)−7 and combining like terms, the resulting equivalent equation is −12d+1, which means the correct answer is 'None of the above.'

Step-by-step explanation:

The student's question asks which equations are equivalent to −4(3d−2)−7. To find the equivalent equation, we distribute the −4 to both terms within the parentheses and then subtract 7. Here's the step-by-step distribution:

• Multiply −4 by 3d to get −12d.
• Multiply −4 by −2 to get +8.
• Combine the +8 with −7 to get +1 (because 8−7 equals 1).
• The resulting equation is −12d+1.

The given expression is −4(3d−2)−7. To simplify this expression, distribute −4 to both terms inside the parentheses.

−4(3d−2)−7 = −12d + 8 − 7

Combine like terms to get:

−12d + 1

Therefore, the equation that is equivalent to −4(3d−2)−7 is −12d + 1 (Option A).

Therefore, the correct answer is None of the above, neither A) −12d−15 nor B) 12d−15 is equivalent to the original expression.