Pre-Algebra
Expressions and equations
Writing and solving inequalities
20 practice questions
0 video lessons
Theory + worked examples
Writing and Solving Inequalities
Texas Pre-Algebra (TEKS) • Standard 7.11(A) • Expressions & Equations
Writing and Solving Inequalities is a topic in Expressions & Equations in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.11(A), which requires students to write and solve one-variable inequalities and graph their solutions.
Inequalities are solved like equations, except the sign flips when you multiply or divide by a negative; solutions are ranges.
Theory
An inequality compares expressions with \(<,\le,>,\ge\) and has a range of solutions.
Solve like an equation, but flip the sign when multiplying or dividing by a negative.
A solution range on a number line.
Solving inequalities.
The flip rule:
\[a<b \implies -a>-b\]
Open circle for \(<,>\); closed for \(\le,\ge\).
How to solve an inequality
- Isolate the variable as in an equation.
- Flip the sign if you multiply/divide by a negative.
- Graph the solution on a number line.
- Use open or closed circles correctly.
Example 1 — One step
Solve \(x+2>5\).
Solution
Subtract \(2\).
| \(x\) | \(>\) | \(3\) |
Example 2 — Divide positive
Solve \(4x\le 12\).
Solution
Divide by \(4\).
| \(x\) | \(\le\) | \(3\) |
Example 3 — Flip the sign
Solve \(-2x<6\).
Solution
Divide by \(-2\) and flip.
| \(x\) | \(>\) | \(-3\) |
Example 4 — Write one
Write: a number \(n\) is at least \(10\).
Solution
“At least” means \(\ge\).
| \(n\) | \(\ge\) | \(10\) |
Common pitfalls
Flip the sign only for a negative multiplier/divisor.
Open vs closed circle depends on \(<\) vs \(\le\).
The solution is a range, not one value.
Frequently asked questions
How is solving an inequality different?
Flip the sign when multiplying or dividing by a negative.
When do I use an open circle?
For strict inequalities \(<\) and \(>\).
Solve \(-2x<6\).
\(x>-3\).
What does 'at least' mean?
\(\ge\).
More in Expressions and equations