Solve $6 x+18=3 x+9$ for $x$.
Answer (2)
Subtract 3 x from both sides: 3 x + 18 = 9 .
Subtract 18 from both sides: 3 x = − 9 .
Divide both sides by 3: x = − 3 .
The solution is − 3 .
Explanation
Understanding the Problem We are given the equation 6 x + 18 = 3 x + 9 and asked to solve for x . This is a linear equation, and we can solve it by isolating x on one side of the equation.
Isolating x terms First, subtract 3 x from both sides of the equation to get the x terms on one side:
6 x + 18 − 3 x = 3 x + 9 − 3 x
This simplifies to:
3 x + 18 = 9
Isolating the x term Next, subtract 18 from both sides of the equation to isolate the x term:
3 x + 18 − 18 = 9 − 18
This simplifies to:
3 x = − 9
Solving for x Finally, divide both sides of the equation by 3 to solve for x :
3 3 x = 3 − 9
This simplifies to:
x = − 3
Final Answer Therefore, the solution to the equation 6 x + 18 = 3 x + 9 is x = − 3 .
Examples
Linear equations are used in various real-life scenarios, such as calculating the cost of items, determining distances, and converting between different units. For example, if you want to determine how many hours you need to work to earn a certain amount of money, you can set up a linear equation to model the situation and solve for the number of hours. Suppose you earn $15 per hour and need to earn $300. The equation would be 15 h = 300 , where h is the number of hours. Solving for h gives h = 20 hours.
To solve the equation 6 x + 18 = 3 x + 9 , we isolate the variable by subtracting terms and eventually find that x = − 3 .
;
