➕ Algebra 1 · Inequalities
Solving Inequalities flashcards
Say the answer out loud before you flip. Cards you miss come back sooner; cards you know come back later. That spacing is what builds long-term memory.
All 16 flashcards at a glance
Card 1
On a number line, what is the difference between an open circle and a closed circle?
An open circle (for < and >) means the boundary number is not a solution. A closed circle (for ≤ and ≥) means the boundary number is a solution.
Card 2
Write “the balance b is at most 250 dollars” as an inequality.
b ≤ 250. “At most” means 250 or less, so 250 itself is allowed.
Card 3
Write “a number n is more than 12” as an inequality. Is 12 a solution?
n > 12. No: 12 is not more than 12, so the circle is open.
Card 4
Solve x − 9 < −2.
x < 7. Add 9 to both sides. The sign stays. (Check: x = 0 gives −9 < −2, which is true.)
Card 5
Solve 4x ≥ −36.
x ≥ −9. Divide both sides by 4, which is positive, so the sign stays.
Card 6
Solve −6x > 48.
x < −8. Divide both sides by −6 and reverse the sign. (Check: x = −10 gives 60 > 48, which is true.)
Card 7
Solve 15 − 2x > 1.
x < 7. Subtract 15: −2x > −14. Divide by −2 and reverse the sign: x < 7.
Card 8
Solve (3/4)x ≥ 9.
x ≥ 12. Multiply both sides by 4/3, which is positive, so the sign stays.
Card 9
Solve 2(x + 3) ≤ 4x − 10.
x ≥ 8. Distribute: 2x + 6 ≤ 4x − 10. Subtract 2x: 6 ≤ 2x − 10. Add 10: 16 ≤ 2x. Divide by 2: 8 ≤ x, which is the same as x ≥ 8.
Card 10
Why does the sign reverse when you multiply both sides by a negative number?
Multiplying by a negative number mirrors the number line across 0, so the order of two numbers swaps. Example: 1 < 4, but after multiplying both sides by −3 you get −3 > −12.
Card 11
What happens to the sign when you add or subtract the same number on both sides?
Nothing. The sign stays. For example, adding 10 to both sides of x − 10 < 3 gives x < 13.
Card 12
How many solutions does x > 10 have, if x can be any real number?
Infinitely many: every real number greater than 10. There is no smallest one (10.1, 10.01 and 10.001 all work).
Card 13
The variable terms cancel and you are left with 3 < 8. What does that mean?
3 < 8 is true, so every real number is a solution.
Card 14
The variable terms cancel and you are left with 4 < 4. What does that mean?
4 < 4 is false, so there is no solution. (With ≤ you would get 4 ≤ 4, which is true.)
Card 15
How can you check a solved inequality such as x ≤ 9?
Put these into the original inequality: a number from the shaded part (it should be true), a number from the unshaded part (it should be false), and the boundary 9 (both sides come out equal, and it counts because of the ≤).
Card 16
In this lesson’s FLIP memory trick, what do the letters stand for?
Find the number you multiply or divide both sides by. Look at its sign. If it is negative, Put in the reversed sign.