What is a Linear Equation?
A linear equation is an equation that can be written in the form
$$
ax + b = c
$$
where $x$ is the variable, and $a$, $b$, and $c$ are constants. The solution is the value of $x$ that makes the equation true.
Step-by-Step Example
Solve:
$$
3x - 5 = 10
$$
Step 1: Isolate the variable term
Add $5$ \to both sides \to move the constant: %%MATH_DISPLAY_2%% %%MATH_DISPLAY_3%% **Step 2: Solve for $x$** Divide both sides by $3$: %%MATH_DISPLAY_4%% %%MATH_DISPLAY_5%% **Step 3: Check your solution** Substitute $x = 5$ back into the original equation: %%MATH_DISPLAY_6%% The solution checks out. --- ## Takeaways - To solve a linear equation, isolate the variable using inverse operations (addition, subtraction, multiplication, division). - Always check your solution by substituting it back into the original equation. - Linear equations have at most one solution for $x$.