solve for x to determine if the equation has one, none, or infinite solutions.

Question

4x = 3(x + 5) - 15
a the equation has one solution x = -10
b the equation has one solution: x = 0
c the equation has infinite solutions
d the equation has no solution

Answer 1

To determine if the equation has one, none, or infinite solutions, we need to simplify and solve for x.

Starting with the given equation:
4x = 3(x + 5) - 15

First, we distribute 3 into (x + 5):
4x = 3x + 15 - 15

Next, we combine like terms on the right side:
4x = 3x

Now, we subtract 3x from both sides to isolate x on one side:
4x - 3x = 0

Simplifying, we get:
x = 0

Therefore, the equation has one solution: x = 0.

The correct answer is b) the equation has one solution: x = 0.