Question

Solve 0.5(−2 4d) − 2d = −13 for d.

a) Infinite solutions
b) No solution
c) d = −11
d) d = 1.375

Answer 1

The equation 0.5(−2 + 4d) − 2d = −13 simplifies to a false statement (−1 = −13), indicating that there is no solution to the equation. Option B is correct.

Step-by-step explanation:

To solve the equation 0.5(−2 + 4d) − 2d = −13 for d, begin by distributing the 0.5 to terms within the parentheses:

0.5(−2) + 0.5(4d) − 2d = −13

−1 + 2d − 2d = −13

Since 2d − 2d equals zero, the equation simplifies to:

−1 = −13

This statement is false since negative one does not equal negative thirteen. Hence, there is no solution to the equation, as the two sides of the equation will never be equal. We can conclude that the answer is (b) No solution.

To solve the equation 0.5(-2+4d) - 2d = -13 for d, we follow these steps:

Distribute 0.5 to the terms inside the parentheses: -1+2d - 2d = -13.

Combine like terms: -1 = -13.

The equation is not true, so there is no solution.