Solving Linear Equations and Checking Solutions

Q1. Solve the equation and check your solution:

$7x - 64 - 15x = 4x + 64 + 4x$

Background

Topic: Linear Equations

This question tests your ability to solve a linear equation by combining like terms, isolating the variable, and checking your solution by substitution.

Key Terms and Formulas

• Linear equation: An equation involving only the first power of the variable.

• Combining like terms: Adding or subtracting terms with the same variable.

• Isolating the variable: Manipulating the equation to get the variable alone on one side.

Step-by-Step Guidance

1. Combine like terms on both sides of the equation. On the left, $7x - 15x$; on the right, $4x + 4x$.

2. Rewrite the equation after combining like terms: $-8x - 64 = 8x + 64$.

3. Subtract $8x$ from both sides to start isolating $x$.

4. Simplify the equation after subtraction.

Try solving on your own before revealing the answer!

Final Answer: $x = -8$

After isolating $x$, you get $-16x = 128$, so $x = -8$.

Substitute $x = -8$ back into the original equation to check: both sides equal $0$, confirming the solution is correct.