Final answer:
To solve the equation -4x + 3(5x + 6) = 7(2x + 1) - 3x, the terms are expanded and simplified, which results in x = -1. Checking the solution confirms that it is correct and reasonable.
Step-by-step explanation:
To solve the equation -4x + 3(5x + 6) = 7(2x + 1) - 3x, we need to expand and simplify it first:
Distribute the 3 across (5x + 6): -4x + 15x + 18.
Distribute the 7 across (2x + 1): 14x + 7.
Combine like terms on each side: 11x + 18 = 14x + 7 - 3x.
Simplify further by adding 4x and subtracting 18 from both sides: 11x - 4x = 7 - 18.
Combine like terms again: 7x = -11.
Divide both sides by 7 to find the value of x: x = -±7/7.
Simplify the fraction: x = -1.
After simplifying the equation, we found that x = -1. We can check this solution by substituting -1 back into the original equation to verify that both sides are equal. This confirms that the solution is reasonable.