Solving Linear Equations

Linear equations are equations of the first degree, which means they contain variables raised only to the first power. The general form of a linear equation in one variable is given by: $ax + b = 0$ where $a$ and $b$ are constants, and $x$ is the variable we want to solve for.

Steps to Solve Linear Equations:

1. Isolate the variable on one side of the equation.
2. Perform inverse operations to both sides to maintain equality.
3. Simplify the equation to find the value of the variable.

Example:

Solve the equation:

$$3x + 5 = 14$$

Step 1: Subtract 5 from both sides:

$$3x + 5 - 5 = 14 - 5$$ $$3x = 9$$

Step 2: Divide both sides by 3:

$$\frac{3x}{3} = \frac{9}{3} \newline$$ $$x = 3$$

The solution is $x = 3$.

Key Questions:

• What is the first step to take when solving $2x + 4 = 12$?
• How would you solve the equation $5x - 7 = 8$?
• If $4x + 9 = 25$, what is the value of $x$?
• Can you explain how to isolate the variable in the equation: $\newline\frac{x}{2} - 3 = 1$?

Keywords:

• Linear equation
• Variable
• Solve
• Isolate
• Constants