Question

The equation the quantity 3x minus 15 divided by 2 equals 4x models temperature change, where x represents the difference in degrees in the last 24 hours. solve for x. x = 11 x = 6 x = −3 x = −15

Answer 1

To solve the equation (3x - 15) / 2 = 4x, algebraic manipulations yield x = -3. Multiplication, subtraction, and division are used in the process to isolate x, and a check confirms that the solution is correct.

Step-by-step explanation:

The student's question involves solving the equation (3x - 15) / 2 = 4x for x, which represents the difference in degrees in temperature change over the last 24 hours. To solve for x, you must perform algebraic manipulations. Here are the steps:

Multiply both sides of the equation by 2 to get rid of the fraction: 3x - 15 = 8x.

Subtract 3x from both sides to get all x terms on one side: -15 = 5x.

Divide both sides by 5 to isolate x: x = -3.

Therefore, the value of x that solves the equation is x = -3.

To check if the answer makes sense, substitute x with -3 in the original equation: (3(-3) - 15) / 2 = 4(-3). This simplifies to (-9 - 15) / 2 = -12, which further simplifies to -24 / 2 = -12, confirming that -12 equals -12, hence x = -3 is correct.