How many solutions does the equation have? 8 + 3(𝑥 − 6) = −2 + 3𝑥 − 4 R. one solution S. infinite solutions T. no solution

5 answers

R. one solution

wrong

T. no solution

please explain

To determine if an equation has no solution, we need to simplify it and see if it leads to a contradiction.

Given equation: 8 + 3(x - 6) = -2 + 3x - 4

First, distribute the 3 on the left side:
8 + 3x - 18 = -2 + 3x - 4

Combine like terms on both sides:
3x - 10 = 3x - 6

Subtract 3x from both sides and simplify:
-10 = -6

However, -10 does not equal -6, therefore this equation leads to a contradiction. This means that there is no solution to the original equation.