Question

How many solutions exist for the given equation: 4(x-1) = 17 + x?

a) No solution
b) One solution
c) Two solutions
d) Infinite solutions

Answer 1

The equation 4(x-1) = 17 + x has one solution, which is x = 7, after simplifying and solving the equation.

Step-by-step explanation:

To determine how many solutions exist for the equation 4(x-1) = 17 + x, we can simplify and solve for x:

1. Distribute the 4 into the parentheses: 4x - 4 = 17 + x.
2. Subtract x from both sides to get all x terms on one side: 3x - 4 = 17.
3. Add 4 to both sides to isolate the x terms: 3x = 21.
4. Divide both sides by 3 to solve for x: x = 7.

Since we have found a single value for x that satisfies the equation, there is one solution.