Solve the equation $3(x+1)-2=x+5$
Answer (1)
Expand the left side of the equation: 3 ( x + 1 ) − 2 = 3 x + 3 − 2 = 3 x + 1 .
Rewrite the equation as 3 x + 1 = x + 5 .
Subtract x from both sides: 2 x + 1 = 5 .
Subtract 1 from both sides: 2 x = 4 .
Divide both sides by 2: x = 2 .
The solution is 2 .
Explanation
Understanding the Problem We are given the equation 3 ( x + 1 ) − 2 = x + 5 and asked to solve for x . We will simplify and isolate x to find the solution.
Expanding the Equation First, we expand the left side of the equation: 3 ( x + 1 ) − 2 = 3 x + 3 − 2 = 3 x + 1 . So the equation becomes 3 x + 1 = x + 5 .
Subtracting x from Both Sides Next, we subtract x from both sides of the equation: 3 x − x + 1 = x − x + 5 , which simplifies to 2 x + 1 = 5 .
Subtracting 1 from Both Sides Then, we subtract 1 from both sides of the equation: 2 x + 1 − 1 = 5 − 1 , which simplifies to 2 x = 4 .
Dividing by 2 Finally, we divide both sides of the equation by 2: 2 2 x = 2 4 , which simplifies to x = 2 .
Final Answer Therefore, the solution to the equation 3 ( x + 1 ) − 2 = x + 5 is x = 2 .
Examples
Imagine you're planning a birthday party and need to figure out how many guests you can invite. You have a budget of $50, and each guest costs you $5 for food and drinks, plus a fixed cost of $10 for the venue. If you set up the equation 5 x + 10 = 50 , where x is the number of guests, solving for x will tell you the maximum number of guests you can invite without exceeding your budget. This type of problem helps in everyday budgeting and planning scenarios.
