Solve for $x$.
$6(x-1)=9(x+2)$
Answer (1)
Expand both sides of the equation: 6 x − 6 = 9 x + 18 .
Simplify the equation by subtracting 6 x from both sides: − 6 = 3 x + 18 .
Isolate x by subtracting 18 from both sides: − 24 = 3 x .
Solve for x by dividing both sides by 3: x = − 8 . The final answer is − 8 .
Explanation
Understanding the problem We are given the equation 6 ( x − 1 ) = 9 ( x + 2 ) and we want to solve for x .
Expanding both sides First, we expand both sides of the equation: 6 ( x − 1 ) = 6 x − 6 9 ( x + 2 ) = 9 x + 18
Setting up the equation Now we set the expanded expressions equal to each other: 6 x − 6 = 9 x + 18
Isolating x Next, we want to isolate x on one side of the equation. We can subtract 6 x from both sides: 6 x − 6 − 6 x = 9 x + 18 − 6 x − 6 = 3 x + 18
Continue isolating x Now, subtract 18 from both sides: − 6 − 18 = 3 x + 18 − 18 − 24 = 3 x
Solving for x Finally, divide both sides by 3 to solve for x :
3 − 24 = 3 3 x x = − 8
Final Answer Therefore, the solution is x = − 8 .
Examples
In real-world scenarios, solving linear equations like this can help determine break-even points in business, calculate the required amount of ingredients in recipes, or find the intersection point of two lines in geometry. For example, if you have two different phone plans with different monthly fees and per-minute charges, you can set up a linear equation to find out at what number of minutes the two plans cost the same.
