Solve for x.
$7 x+12=5(x+6)$
Answer (2)
The solution to the equation 7 x + 12 = 5 ( x + 6 ) is found by first expanding and rearranging the terms. After isolating x, we find that x = 9 .
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Expand the right side of the equation: 7 x + 12 = 5 x + 30 .
Subtract 5 x from both sides: 2 x + 12 = 30 .
Subtract 12 from both sides: 2 x = 18 .
Divide both sides by 2: x = 9 . The solution is 9 .
Explanation
Understanding the Problem We are given the equation 7 x + 12 = 5 ( x + 6 ) and our goal is to find the value of x that satisfies this equation.
Expanding the Equation First, we need to expand the right side of the equation by distributing the 5 across the terms inside the parentheses:
7 x + 12 = 5 × x + 5 × 6
7 x + 12 = 5 x + 30
Isolating x Terms Next, we want to isolate the terms with x on one side of the equation and the constant terms on the other side. We can subtract 5 x from both sides of the equation:
7 x − 5 x + 12 = 5 x − 5 x + 30
2 x + 12 = 30
Isolating the x Term Now, we subtract 12 from both sides of the equation to isolate the term with x :
2 x + 12 − 12 = 30 − 12
2 x = 18
Solving for x Finally, we divide both sides of the equation by 2 to solve for x :
2 2 x = 2 18
x = 9
Final Answer Therefore, the solution to the equation 7 x + 12 = 5 ( x + 6 ) is x = 9 .
Examples
Imagine you're trying to figure out how many hours you need to work this week to afford a new video game. You know you earn $7 per hour and already have $12 saved. The game costs $5 per hour of gameplay plus a $6 activation fee. By setting up the equation 7 x + 12 = 5 ( x + 6 ) , where x is the number of hours you work, you can solve for x to find out how many hours you need to work to afford the game. This type of problem helps in budgeting and making financial decisions.
