Question

Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions.

Equation 1: 5x + 61 = 41
Equation 2: 2x + 131 = 28
a) The solutions are equal.
b) The solutions are not real numbers.
c) The solutions are different real numbers.
d) There are no solutions to these equations.

Answer 1

To solve Equation 1, subtract 61 from both sides and then divide by 5. To solve Equation 2, subtract 131 from both sides and then divide by 2. The solutions are -4 and -51.5, respectively, and they are different real numbers.

Step-by-step explanation:

To solve Equation 1, we need to isolate the variable x. We can do this by subtracting 61 from both sides of the equation: 5x = 41 - 61 = -20. Then, we divide both sides of the equation by 5 to solve for x: x = -20/5 = -4.

Now, let's solve Equation 2. First, we subtract 131 from both sides of the equation: 2x = 28 - 131 = -103. Then, we divide both sides of the equation by 2 to solve for x: x = -103/2 = -51.5.

Comparing the solutions, we can see that the solution to Equation 1 is -4 and the solution to Equation 2 is -51.5. Therefore, the statement that is true about both solutions is: c) The solutions are different real numbers.