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:
Plan to Solve for the Variable
- Combine like terms on the left-hand side.
- Simplify the resulting expression.
- Isolate the variable term.
- Solve for the variable.
- Check the solution by substituting it back into the original equation.
Step-by-Step Solution
Given Equation:
–2x – 4 + 5x = 8
Step 1: Combine like terms (–2x and 5x)
(–2x + 5x) – 4 = 8
3x – 4 = 8
Step 2: Add 4 to both sides to isolate the variable term
3x – 4 + 4 = 8 + 4
3x = 12
Step 3: Divide both sides by 3 to solve for x
3x ÷ 3 = 12 ÷ 3
x = 4
Explanation
To solve the linear equation –2x – 4 + 5x = 8, the first step is to simplify the left side of the equation by combining like terms. The variable terms –2x and 5x both contain x, so they can be added together. When you combine –2x and 5x, the result is 3x. This simplifies the equation to 3x – 4 = 8.
Next, we need to isolate the term containing the variable. To do this, add 4 to both sides of the equation. This eliminates the constant –4 on the left-hand side. Adding 4 to both sides gives us 3x = 12.
Now that we have 3x = 12, we solve for x by dividing both sides of the equation by 3. This step removes the coefficient of the variable x. When we divide 3x by 3, we get x. Similarly, 12 divided by 3 gives 4. So, the value of x is 4.
To ensure the solution is correct, we can check by substituting x = 4 back into the original equation. Replacing x with 4, the left-hand side becomes –2(4) – 4 + 5(4), which simplifies to –8 – 4 + 20. This equals 8, which matches the right-hand side of the equation. Since both sides are equal, x = 4 is the correct solution.
This step-by-step method demonstrates how combining like terms and isolating the variable leads to the correct answer.
