To solve for x from the equation 3x – 13 = 7(x + 2) - 4(x - 7), we just have to follow these steps:
1. distribute the products of the right side to get rid of the parentheses
3x - 13 = 7(x + 2) - 4(x - 7)
3x - 13 = 7*x + 7*2 - 4*x - 4*7
3x - 13 = 7x + 14 - 4x - 28
2. Combine like terms on the right side:
3x - 13 = 7x - 4x + 14 - 28
3x - 13 = 3x - 14
3. Subtract 3x on both sides:
3x - 3x -13 = 3x - 3x - 14
-13 ≠ -14
As you can see, we eliminated all the x-variables in the equation, now we can't get a solution, also the equality is false since -13 is not equal to -14, then we can conclude that this equation has no solution