1. We first simplify both sides of the equation, factoring the parentheses and adding like numbers:
[tex]5x - (x + 3) = \frac{1}{3} (9x + 18) - 5 \\ 5x - x - 3 = 3x + 6 - 5 \\ 4x - 3 = 3x + 1[/tex]
Then, we move all the Xs to one side and all the numbers to the other by subtracting 3x from both sides and adding 3 to both sides:
[tex]4x - 3 = 3x + 1 \\ 4x - 3x = 1 + 3 \\ x = 4[/tex]
We get x = 4.
2. First, we simplify:[tex]5(3x + 9) - 2x = 15x - 2(x - 5) \\ 15x + 45 - 2x = 15x - 2x + 10 \\ 13x + 45 = 13x + 10[/tex]
Then, we try to move the Xs to one side, but we get 13x - 13x, which equals 0x. This problem is impossible, as it states 45 = 10.
