Grade 6 Equations

Interactive step-by-step solver for understanding and solving simple linear equations.

Grade 6 Equations
Learning Mode
Practice Mode
Related Concepts

Step-by-Step Learning

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 \( x = 7 \).
Solving \( x + 5 = 12 \) Subtract 5: \( x + 5 - 5 = 12 - 5 \) Simplify: \( x = 7 \) Verify: \( 7 + 5 = 12 \)

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 \( x = 6 \).
Solving \( 3x = 18 \) Divide by 3: \( \frac{3x}{3} = \frac{18}{3} \) Simplify: \( x = 6 \) Verify: \( 3 \times 6 = 18 \)

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 \( x = 3 \).
Solving \( 2x + 4 = 10 \) Subtract 4: \( 2x + 4 - 4 = 10 - 4 \) Simplify: \( 2x = 6 \), Divide by 2: \( x = 3 \) Verify: \( 2 \times 3 + 4 = 10 \)

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.