2.4 solving multi-step inequality NOTES and Homework

To solve a multi-step inequality, you can follow these steps:

1. Distribute any coefficients in front of parentheses.

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

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

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

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

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 inequality:

2x < 8

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

x < 4

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

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 inequalities:

• Forgetting to distribute coefficients in front of parentheses.

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

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

• Making careless mistakes when performing the arithmetic.

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

By following these steps, you can solve multi-step inequalities correctly and confidently.

Here are some additional tips for solving multi-step inequalities:

• Be careful with the order of operations. When you are adding or subtracting terms, you must do so before you multiply or divide.

• Remember that when you multiply or divide by a negative number, you must reverse the inequality sign.

• If you are unsure whether your solution is correct, you can always check it by substituting it back into the original inequality.