Final answer:
The equation 2(3x-6)=3(x+3) is solved by first expanding both sides and then isolating the variable x. After simplification and solving, the value x = 7 is found, which can be checked and confirmed by substituting back into the original equation.
Step-by-step explanation:
To solve the equation 2(3x−6)=3(x+3), we must first expand both sides to eliminate any parentheses. By distributing the numbers outside the parentheses, the equation becomes 6x − 12 = 3x + 9. Next, we aim to isolate the variable x by moving like terms to one side and constants to the other side. Subtract 3x from both sides to get 3x − 12 = 9, and then add 12 to both sides to obtain 3x = 21. Finally, divide both sides by 3 to find that x = 7.
Step 6, as referenced in the provided information, advises to eliminate terms wherever possible to simplify the algebra. We've done this by expanding and then combining like terms. For Step 7, it suggests checking if the answer is reasonable. Upon revising the original equation with x = 7, we can see that both sides of the equation equal 21, confirming that our solution is reasonable.
By simplifying complicated expressions and eliminating terms, as described in the various steps, we have successfully solved for x in a step-by-step manner, showcasing that algebra can be tackled by breaking down equations into simpler parts and applying basic arithmetic operations.