Solve for x: 3(x+1)=5(x−2)+7

Begin by distributing the 3 and the 5 through their respective parentheses, then combine like terms on each side of the equal sign:
3(x+1)=5(x−2)+7
3x+3=5x−10+7
3x+3=5x−3
Add 3 to both sides to maintain the equality:
3x+6=5x
Subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:
6=2x
3=x
Remember that any time a variable is solved for in an equation, the calculated value can be verified by substituting it into the original equation and determining whether it yields a true statement.