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

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

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

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

Flashcard 3: What inequality represents a number $x$ is less than $10$?

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

Flashcard 4: What is the solution set for $5x + 2 \neq 12$?

Answer: $x \neq 2$. Subtract 2, divide by 5 to find excluded value.

Flashcard 5: Solve $-3x + 7 \neq 1$ for $x$.

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

Flashcard 6: Solve $0 < 2x + 4$ for $x$.

Answer: $x > -2$. Subtract 4, divide by 2 to solve inequality.

Flashcard 7: 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 8: What inequality symbol represents 'greater than or equal to'?

Answer: $\geq$. Combines greater than and equal to in one symbol.

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

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

Flashcard 10: Find the value of $x$ in $5x - 3 < 2x + 6$.

Answer: $x < 3$. Move $2x$ left and $-3$ right, then divide by 3.

Flashcard 11: Solve $-5x \neq 10$ for $x$.

Answer: $x \neq -2$. Divide both sides by -5 to isolate $x$.

Flashcard 12: Identify the inequality symbol for 'greater than'.

Answer: $>$. Symbol for strict inequality without equality.

Flashcard 13: Find the value of $x$ in $5x - 3 < 2x + 6$.

Answer: $x < 3$. Move $2x$ left and $-3$ right, then divide by 3.

Flashcard 14: What is the solution to the inequality $2x + 3 > 7$?

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

Flashcard 15: Identify the solution set for $2x + 5 > 9$.

Answer: The solution set is $x > 2$. Subtract 5 from both sides, then divide by 2.

Flashcard 16: Determine if $x = -1$ satisfies $2x + 3 > 0$.

Answer: No, $x = -1$ does not satisfy $2x + 3 > 0$. Substituting gives $2(-1) + 3 = 1 > 0$ is false.

Flashcard 17: 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 18: Which symbol represents 'greater than or equal to'?

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

Flashcard 19: What inequality represents a number $x$ is less than $10$?

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

Flashcard 20: Determine if $x = -1$ satisfies $2x + 3 > 0$.

Answer: No, $x = -1$ does not satisfy $2x + 3 > 0$. Substituting gives $2(-1) + 3 = 1 > 0$ is false.

Flashcard 21: What is the solution to the inequality $2x + 3 > 7$?

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

Flashcard 22: What is the solution to $4 - x > 8$?

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

Flashcard 23: Solve for $x$: $3(x - 2) \geq 9$.

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

Flashcard 24: Solve $8 - x \neq 5$ for $x$.

Answer: $x \neq 3$. Solve $x = 3$ from the equation $8 - x = 5$.

Flashcard 25: What is the solution to $3(x - 2) < 6$?

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

Flashcard 26: Solve the inequality $-2x + 9 < 3$ for $x$.

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

Flashcard 27: 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.

Flashcard 28: What is the inequality for 'y is less than 8'?

Answer: $y < 8$. 'Less than' means strictly smaller than 8.

Flashcard 29: Which symbol represents 'greater than or equal to'?

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

Flashcard 30: 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 31: Solve $-4x + 5 eq -11$ for $x$.

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

Flashcard 32: What is the inequality for 'x is at least 5'?

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

Flashcard 33: What does the inequality $x < 0$ represent?

Answer: Negative numbers. All values to the left of zero on number line.

Flashcard 34: Solve $x - 5 \geq 0$ for $x$.

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

Flashcard 35: 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 36: What is the solution to $x/3 \neq 2$?

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

Flashcard 37: Solve $2x + 3 \leq 7$ for $x$.

Answer: $x \leq 2$. Subtract 3, divide by 2 to solve inequality.

Flashcard 38: Solve $4 - 2x \neq 0$ for $x$.

Answer: $x \neq 2$. Solve $2x = 4$ to find the excluded value.

Flashcard 39: What is the inequality for 'x is more than 10'?

Answer: $x > 10$. 'More than' means strictly greater than.

Flashcard 40: 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 41: Solve $7x - 3 \neq 25$ for $x$.

Answer: $x \neq 4$. Add 3, divide by 7 to find excluded value.

Flashcard 42: Solve $3x + 7 \leq 16$ for $x$.

Answer: $x \leq 3$. Subtract 7, divide by 3 to isolate $x$.

Flashcard 43: What is the solution set for $3(x - 4) < 6$?

Answer: $x < 6$. Distribute 3, add 12, then divide by 3.

Flashcard 44: Solve $-3(x + 4) \neq 9$ for $x$.

Answer: $x \neq -7$. Distribute -3, subtract 12, divide by -3.

Flashcard 45: What inequality symbol represents 'less than or equal to'?

Answer: $\leq$. Combines less than and equal to in one symbol.

Flashcard 46: 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 47: What is the solution to $x + 3 > 10$?

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

Flashcard 48: 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 49: What is the solution to $4 - x > 8$?

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

Flashcard 50: 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 51: What is the inequality representation of 'p is at most 4'?

Answer: $p \leq 4$. 'At most' means less than or equal to.

Flashcard 52: 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 53: 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 54: Identify the solution set for $2x + 5 > 9$.

Answer: The solution set is $x > 2$. Subtract 5 from both sides, then divide by 2.

Flashcard 55: 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 56: 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 57: State the inequality that represents $x$ is at most 7.

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

Flashcard 58: Solve $6(x - 2) > 12$ for $x$.

Answer: $x > 4$. Distribute 6, add 12, then divide by 6.

Flashcard 59: Solve $5 - 2x \neq 13$ for $x$.

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

Flashcard 60: State the inequality that represents $x$ is at most 7.

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

Flashcard 61: 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 62: 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.