Definition
A simple linear equation is an equation of the form:
$$ ax + b = c $$
where $x$ is the variable, and $a$, $b$, and $c$ are constants. The goal is to find the value of $x$ that makes the equation true.
Worked Example
Solve: $3x + 5 = 14$ **Step 1:** Subtract $5$ from both sides \to isolate the term with $x$: %%MATH_DISPLAY_1%% **Step 2:** Divide both sides by $3$ \to solve for $x$: %%MATH_DISPLAY_2%% **Check:** Substitute $x = 3$ back into the original equation:
$$ 3(3) + 5 = 9 + 5 = 14 $$
The solution is correct.
Key Takeaways
- Isolate the variable by performing inverse operations (addition/subtraction, multiplication/division).
- Always perform the same operation on both sides of the equation to maintain equality.
- Check your solution by substituting it back into the original equation.