SAT Math Flashcards: Linear Inequalities

What this deck covers

This deck focuses on Linear Inequalities, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: State the inequality that represents $x$ is at most 7.

Answer: $x \leq 7$. 'At most' means less than or equal to.

Flashcard 2: What inequality represents a number $x$ is less than $10$?

Answer: $x < 10$. Standard notation for values below 10.

Flashcard 3: How would you express $4$ is less than or equal to $x$?

Answer: $4 \leq x$. Reverses the typical order to show 4 as the lesser value.

Flashcard 4: What is the solution to the inequality $2x + 3 > 7$?

Answer: $x > 2$. Subtract 3 from both sides, then divide by 2.

Flashcard 5: What is the solution to the inequality $-3x \neq 9$?

Answer: $x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.

Flashcard 6: What is the solution to $4 - x > 8$?

Answer: $x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.

Flashcard 7: Solve for $x$: $3(x - 2) \geq 9$.

Answer: $x \geq 5$. Distribute 3, add 6 to both sides, then divide by 3.

Flashcard 8: What is the graphical representation of $y \neq 4$?

Answer: A horizontal line at $y = 4$ with a dashed line. Uses dashed line since $\neq$ excludes the boundary value.

Flashcard 9: How would you express $4$ is less than or equal to $x$?

Answer: $4 \leq x$. Reverses the typical order to show 4 as the lesser value.

Flashcard 10: Which symbol represents 'greater than or equal to'?

Answer: $\geq$. Standard mathematical symbol for greater than or equal to.

Flashcard 11: What is the solution to $3(x - 2) < 6$?

Answer: $x < 4$. Distribute 3, add 6 to both sides, then divide by 3.

Flashcard 12: What is the solution to the inequality $-3x \neq 9$?

Answer: $x \neq -3$. Divide both sides by $-3$, keeping the not-equal sign.

Flashcard 13: What is the solution to $4 - x > 8$?

Answer: $x < -4$. Subtract 4 from both sides, then divide by $-1$ and flip sign.

Flashcard 14: State the rule for reversing an inequality sign.

Answer: Multiply or divide both sides by a negative number. This operation changes the direction of the inequality.

Flashcard 15: Solve the inequality: $-2y + 5 \text{ } \text{≥} \text{ } 11$.

Answer: $y \text{ } \text{≤} \text{ } -3$. Subtract 5, divide by $-2$, and flip the inequality sign.

Flashcard 16: What is the solution to the inequality $2x + 3 > 7$?

Answer: $x > 2$. Subtract 3 from both sides, then divide by 2.

Flashcard 17: What is the solution to $3(x - 2) < 6$?

Answer: $x < 4$. Distribute 3, add 6 to both sides, then divide by 3.

Flashcard 18: Solve the inequality: $5x - 4 \text{ } \text{≤} \text{ } 11$.

Answer: $x \text{ } \text{≤} \text{ } 3$. Add 4 to both sides, then divide by 5.

Flashcard 19: What does the inequality $x \text{ } \text{≤} \text{ } 0$ indicate about $x$?

Answer: $x$ is less than or equal to zero. The variable can be zero or any negative value.

Flashcard 20: Solve the inequality $-2x + 9 < 3$ for $x$.

Answer: $x > 3$. Subtract 9, divide by -2, flip inequality sign.

Flashcard 21: What is the solution to $x + 3 > 10$?

Answer: $x > 7$. Subtract 3 from both sides to isolate $x$.

Flashcard 22: What is the solution to $x/3 \neq 2$?

Answer: $x \neq 6$. Multiply both sides by 3 to isolate $x$.

Flashcard 23: Solve $-3x + 7 \neq 1$ for $x$.

Answer: $x \neq 2$. Subtract 7, divide by -3 to get $x = 2$.

Flashcard 24: What is the solution to $4x + 8 < 16$?

Answer: $x < 2$. Subtract 8, divide by 4 to solve inequality.

Flashcard 25: How do you graph $x \leq -2$ on a number line?

Answer: Closed circle at -2, arrow to the left. Closed circle includes -2 in the solution set.

Flashcard 26: What is the inequality for 'x is at least 5'?

Answer: $x \geq 5$. 'At least' means greater than or equal to.

Flashcard 27: Solve $5 - 2x \neq 13$ for $x$.

Answer: $x \neq -4$. Subtract 5, divide by -2 to get $x = -4$.

Flashcard 28: Solve $-4x + 5 eq -11$ for $x$.

Answer: $x eq 4$. Add 11, divide by -4 to get $x = 4$.

Flashcard 29: Solve $x - 5 \geq 0$ for $x$.

Answer: $x \geq 5$. Add 5 to both sides to isolate $x$.

Flashcard 30: How do you graph $x > 3$ on a number line?

Answer: Open circle at 3, arrow to the right. Open circle shows 3 is not included.