Algebra

x + 1 < 15

Step-by-step solution with explanation

Final Answer

, or in interval notation

Step-by-step solution

1

Identify the inequality to solve

We need to find all values of x that make this inequality true. Our goal is to get x by itself on one side.
2

Subtract 1 from both sides

To isolate x, we subtract 1 from both sides. Whatever we do to one side, we must do to the other to keep the inequality balanced.
3

Simplify both sides

On the left, 1 - 1 = 0, leaving just x. On the right, 15 - 1 = 14. The solution is all values of x less than 14.
4

Write the solution in interval notation

This means x can be any number less than 14, but NOT equal to 14. The parenthesis shows 14 is not included.

Understanding this problem

Learning Insight

Solving an inequality works just like solving an equation — you isolate the variable using inverse operations. The key difference is that if you ever multiply or divide both sides by a negative number, you must flip the inequality sign. Subtracting a positive number, like we did here, keeps the sign the same.

Quick Tip

Think of the inequality sign as an arrow pointing to the smaller value. After isolating x, just read the answer directly: x < 14 means 'x is any number to the left of 14 on the number line.'

Common Mistake

Students sometimes subtract 1 from only one side, writing x < 15 instead of x < 14. Always apply the same operation to BOTH sides of the inequality.