Consider this equation: -2x – 4 + 5x = 8. Generate a plan to solve for the variable. Describe the steps that will be used.
The Correct Answer and Explanation is:
To solve the equation –2x – 4 + 5x = 8, follow these steps:
Step-by-Step Plan:
- Combine like terms on the left side of the equation.
- Isolate the variable term by moving constants to the other side of the equation.
- Solve for the variable by simplifying and performing basic algebraic operations.
- Check your solution by substituting it back into the original equation.
Solving the Equation:
Given:
–2x – 4 + 5x = 8
Step 1: Combine like terms on the left side.
Combine the x terms:
–2x + 5x = 3x
Now the equation becomes:
3x – 4 = 8
Step 2: Move the constant to the right side.
Add 4 to both sides to isolate the x term:
3x – 4 + 4 = 8 + 4
This simplifies to:
3x = 12
Step 3: Solve for x.
Divide both sides by 3:
3x ÷ 3 = 12 ÷ 3
x = 4
Explanation (300 words):
To solve the linear equation –2x – 4 + 5x = 8, we first focus on simplifying both sides to make it easier to isolate the variable. On the left side, we see two terms that contain x: –2x and 5x. These are considered like terms because they share the same variable raised to the same power. Combining them gives us 3x. The updated equation is 3x – 4 = 8.
Next, we aim to isolate the term with the variable by eliminating the constant term on the same side. The constant –4 is subtracted from 3x. To remove it, we add 4 to both sides of the equation. This keeps the equation balanced. On the left side, –4 and +4 cancel each other, leaving only 3x. On the right side, 8 + 4 equals 12. Now the equation is simplified to 3x = 12.
Finally, to find the value of x, we divide both sides of the equation by 3. This step isolates x, which is our goal when solving for a variable. Dividing 12 by 3 gives us x = 4.
To verify the solution, substitute x = 4 back into the original equation:
–2(4) – 4 + 5(4) = –8 – 4 + 20 = 8, which matches the right side.
Thus, x = 4 is the correct solution.
