Solve the equation: 11x = 24 + 8x
The correct answer and explanation is:
To solve the equation 11x=24+8x11x = 24 + 8x, follow these steps:
Step 1: Move the variable terms to one side
Start by getting all the terms that contain xx on one side of the equation. Subtract 8x8x from both sides: 11x−8x=24+8x−8x11x – 8x = 24 + 8x – 8x
This simplifies to: 3x=243x = 24
Step 2: Isolate xx
Now, divide both sides of the equation by 3 to isolate xx: 3×3=243\frac{3x}{3} = \frac{24}{3}
This simplifies to: x=8x = 8
Step 3: Verify the solution
To ensure that the solution is correct, substitute x=8x = 8 back into the original equation: 11(8)=24+8(8)11(8) = 24 + 8(8)
Simplifying both sides: 88=24+6488 = 24 + 64 88=8888 = 88
Since both sides are equal, the solution is correct.
Explanation:
The equation 11x=24+8x11x = 24 + 8x is a linear equation, meaning it involves variables raised only to the first power. The goal is to isolate xx, which means getting all the terms involving xx on one side and the constants on the other. To do this, you subtract 8x8x from both sides of the equation to get 3x=243x = 24. Then, dividing both sides by 3 gives x=8x = 8. This is a straightforward application of basic algebraic operations: addition, subtraction, and division. Solving linear equations like this one is a key foundational skill in algebra.