Learn about solving simple linear equations through these example problems with detailed step-by-step solutions.
Example 1: Solving a Simple Equation
Solve the equation: \( x + 5 = 12 \).
Step 1: To isolate \( x \), subtract 5 from both sides of the equation.
\( x + 5 - 5 = 12 - 5 \)
Step 2: Simplify both sides.
\( x = 7 \)
Step 3: Verify the solution by substituting \( x = 7 \) back into the original equation.
\( 7 + 5 = 12 \), which is true.
Step 4: Therefore, the solution is \( x = 7 \).
Example 2: Solving an Equation with Multiplication
Solve the equation: \( 3x = 18 \).
Step 1: To isolate \( x \), divide both sides by 3.
\( \frac{3x}{3} = \frac{18}{3} \)
Step 2: Simplify both sides.
\( x = 6 \)
Step 3: Verify the solution by substituting \( x = 6 \) back into the original equation.
\( 3 \times 6 = 18 \), which is true.
Step 4: Therefore, the solution is \( x = 6 \).
Example 3: Solving a Two-Step Equation
Solve the equation: \( 2x + 4 = 10 \).
Step 1: Subtract 4 from both sides to isolate the term with \( x \).
\( 2x + 4 - 4 = 10 - 4 \)
\( 2x = 6 \)
Step 2: Divide both sides by 2 to solve for \( x \).
\( \frac{2x}{2} = \frac{6}{2} \)
\( x = 3 \)
Step 3: Verify the solution by substituting \( x = 3 \) back into the original equation.
\( 2 \times 3 + 4 = 6 + 4 = 10 \), which is true.
Step 4: Therefore, the solution is \( x = 3 \).
Practice Mode
Enter your own linear equation to solve, and get a step-by-step solution.
Note: This basic solver can currently handle simple linear equations in the form \( x + a = b \), \( ax = b \), or \( ax + b = c \) where \( a \), \( b \), and \( c \) are integers or simple decimals, and \( x \) is the variable (e.g., Solve \( x + 5 = 12 \), Solve \( 3x = 18 \), Solve \( 2x + 4 = 10 \)). Enter the equation clearly with \( x \) as the variable.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of equations.
Linear Equations
Equations with a single variable and no exponents, representing straight lines when graphed.
Variables
Symbols (like \( x \)) representing unknown quantities in equations.
Balancing Equations
Performing the same operation on both sides to keep the equation equal while isolating the variable.
Solution Verification
Substituting the solution back into the original equation to confirm it is correct.