Final answer:
The equation 3(2x-7) - 4x = 19 simplifies to 2x - 21 = 19, and further to x = 20 after isolating x. This solution does not match any of the provided options, suggesting a problem with the question or answer choices. It is recommended to confirm the original problem or consult the source.
Step-by-step explanation:
Step-by-Step Solution
To solve the equation 3(2x-7) - 4x = 19, we need to simplify the algebra by distributing and combining like terms, then isolate the variable x.
Distribute 3 into the parenthesis: 3×2x - 3×7 = 6x - 21.
Combine the distributed terms with the rest of the equation: 6x - 21 - 4x = 19.
Combine like terms: 6x - 4x = 2x, so the equation now is 2x - 21 = 19.
Add 21 to both sides of the equation to get 2x = 19 + 21 which simplifies to 2x = 40.
Divide both sides by 2 to get x = 40/2 which simplifies to x = 20. However, this solution is not listed in the options provided (a through d), which indicates a mistake was intentionally included in the problem or there was a transcription error.
Since none of the answer choices match the solution, it may be worth double-checking with your teacher or the source of the problem.
Checking the Solution
Since our solution of x = 20 doesn't match any of the provided answer choices, we should check the original problem for any mistakes or consult the source for clarification.