Solving Linear Equations: Step-by-Step Guidance

Q1. Solve the equation and check: $7x - 4 = 8 + 3x$

Background

Topic: Linear Equations

This question tests your ability to solve a linear equation in one variable by isolating the variable and checking your solution.

Key Terms and Formulas

• Linear Equation: An equation of the form $ax + b = cx + d$ where $a, b, c, d$ are constants.

• Additive Property of Equality: You can add (or subtract) the same value to both sides of an equation without changing its solution.

• Multiplicative Property of Equality: You can multiply (or divide) both sides of an equation by the same nonzero value.

Step-by-Step Guidance

1. $\text{Start by moving the constants to one side. Add 4 to both sides to eliminate the -4:}$

   $7x - 4 + 4 = 8 + 3x + 4$

2. $\text{Simplify both sides:}$

   $7x = 3x + 12$

3. $\text{Get all variable terms on one side by subtracting } 3x \text{ from both sides:}$

   $7x - 3x = 3x + 12 - 3x$

4. $\text{Simplify again:}$

   $4x = 12$

Try solving on your own before revealing the answer!

Final Answer: $x = 3$

$\text{Divide both sides by 4:}$

$x = \frac{12}{4} = 3$

To check, substitute $x = 3$ back into the original equation: $7(3) - 4 = 8 + 3(3)$. Both sides equal 17, confirming the solution.