Solve two-step inequalities · lesson

Solve it like an equation

💡 Use the same two undo steps as an equation, and keep the inequality sign.

An inequality uses <, >, ≤, or ≥ instead of =. The answer is a range of numbers.

Solve it like an equation: undo adding or subtracting, then undo multiplying or dividing.

When you type the answer, write ≥ as >= and ≤ as <=.

🧠 Let's work it out

Solve 2x − 7 ≥ 11.

What do you think comes next?

💡 When you multiply or divide both sides by a negative number, flip the inequality sign.

Multiplying or dividing by a negative number reverses the order of numbers. 2 < 5, but −2 > −5.

So if you divide or multiply both sides by a negative, flip the sign: < becomes >, ≤ becomes ≥.

Adding or subtracting never flips the sign.

🧠 Let's work it out

Solve −4x + 3 ≤ 23.

What do you think comes next?

💡 "At most" means ≤ and "at least" means ≥; then round to a whole number that still works.

"At most" or "no more than" means ≤. "At least" or "no less than" means ≥.

Some answers must be whole numbers, like tickets or hours. Solve, then pick the whole number that still fits.

For the greatest number, round down. For the least number, round up.

🧠 Let's work it out

Books cost $8 each with a $5 coupon off the total. You can spend at most $60. How many books can you buy?

Write the inequality: 8n − 5 ≤ 60.
Add 5: 8n ≤ 65.
Divide by 8: n ≤ 8.125, so the greatest whole number is 8.
Another example: to earn at least $130 at $12 an hour, h ≥ 10.83, so round up to 11 hours.

What do you think comes next?