Question

5x+8+12x=4x+3 Lucas claims there are infinitely many solutions. is Lucas claim

a. True
b. False

Answer 1

Lucas's claim that there are infinitely many solutions to the equation 5x + 8 + 12x = 4x + 3 is false. Upon simplifying and solving the equation, a unique solution is found: x = -5/13.

Step-by-step explanation:

To determine if Lucas's claim that there are infinitely many solutions to the equation 5x + 8 + 12x = 4x + 3 is true or false, we need to simplify and solve the equation.

First, we combine like terms on the left side of the equation:

• 5x + 12x + 8 = 4x + 3
• 17x + 8 = 4x + 3

Next, we move all terms involving x to one side and constants to the other:

• 17x - 4x = 3 - 8
• 13x = -5

Now we solve for x:

• x = -5/13

Since we have found a unique solution for x, Lucas's claim is proven to be false. There is only one solution to the equation, which is x = -5/13.