Alg1 - 1.3 Solving Multi-step Equation

To solve a multi-step equation in linear form, you can follow these steps:

1. Distribute any coefficients in front of parentheses.

2. Combine any like terms on both sides of the equation.

3. Isolate the variable on one side of the equation by adding or subtracting terms to both sides of the equation.

4. Divide both sides of the equation by the coefficient of the variable to isolate the variable.

5. Check your solution by substituting it back into the original equation.

Here is an example:

Solve for x: 2x + 3 = 11

Distribute the coefficient in front of the parentheses:

2x + 3 = 11

Combine like terms on both sides of the equation:

2x = 8

Isolate the variable on one side of the equation by dividing both sides by the coefficient of the variable:

x = 4

Check your solution by substituting it back into the original equation:

2(4) + 3 = 11 8 + 3 = 11

11 = 11

The solution is x = 4.

Here are some common mistakes to avoid when solving multi-step equations:

• Forgetting to distribute coefficients in front of parentheses.

• Not combining like terms on both sides of the equation.

• Isolating the variable on the wrong side of the equation.

• Making careless mistakes when performing the arithmetic.

• Not checking your solution by substituting it back into the original equation.

By following these steps, you can solve multi-step equations in linear form correctly and confidently.