Linear Inequalities - PSAT Math
Card 1 of 30
What is the interval notation for $x\ge 5$?
What is the interval notation for $x\ge 5$?
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$[5,\infty)$. Bracket includes 5; infinity always uses parenthesis.
$[5,\infty)$. Bracket includes 5; infinity always uses parenthesis.
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Which value satisfies $2x+1\le 7$: $x=2$ or $x=4$?
Which value satisfies $2x+1\le 7$: $x=2$ or $x=4$?
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$x=2$. Test: $2(2)+1=5 \le 7$ ✓; $2(4)+1=9 > 7$ ✗.
$x=2$. Test: $2(2)+1=5 \le 7$ ✓; $2(4)+1=9 > 7$ ✗.
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What is the solution to $2(x-3)\ge 4x+2$?
What is the solution to $2(x-3)\ge 4x+2$?
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$x\le -4$. Expand: $2x-6 \ge 4x+2$, isolate x: $-8 \ge 2x$.
$x\le -4$. Expand: $2x-6 \ge 4x+2$, isolate x: $-8 \ge 2x$.
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What is the solution to the compound inequality $-1\le 2x+3<7$?
What is the solution to the compound inequality $-1\le 2x+3<7$?
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$-2\le x<2$. Subtract 3 throughout: $-4 \le 2x < 4$, divide by 2.
$-2\le x<2$. Subtract 3 throughout: $-4 \le 2x < 4$, divide by 2.
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What is the solution to $5-\frac{x}{2}<1$?
What is the solution to $5-\frac{x}{2}<1$?
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$x>8$. Subtract 5: $-\frac{x}{2} < -4$, multiply by -2 and flip.
$x>8$. Subtract 5: $-\frac{x}{2} < -4$, multiply by -2 and flip.
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What is the solution to $\frac{x}{4}-3\ge 2$?
What is the solution to $\frac{x}{4}-3\ge 2$?
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$x\ge 20$. Add 3: $\frac{x}{4} \ge 5$, multiply by 4.
$x\ge 20$. Add 3: $\frac{x}{4} \ge 5$, multiply by 4.
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What is the solution to $-2x+1>9$?
What is the solution to $-2x+1>9$?
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$x<-4$. Subtract 1: $-2x > 8$, divide by -2 and flip sign.
$x<-4$. Subtract 1: $-2x > 8$, divide by -2 and flip sign.
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What is the solution to $3x-5\le 7$?
What is the solution to $3x-5\le 7$?
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$x\le 4$. Add 5: $3x \le 12$, then divide by 3.
$x\le 4$. Add 5: $3x \le 12$, then divide by 3.
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Which region is shaded for $y\le mx+b$: above the line or below the line?
Which region is shaded for $y\le mx+b$: above the line or below the line?
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Below the line. Less than or equal means shade where y-values are at or below.
Below the line. Less than or equal means shade where y-values are at or below.
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Which region is shaded for $y>mx+b$: above the line or below the line?
Which region is shaded for $y>mx+b$: above the line or below the line?
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Above the line. Greater than means shade where y-values exceed the line.
Above the line. Greater than means shade where y-values exceed the line.
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Identify the graph boundary type for $y\le -x+3$: solid line or dashed line?
Identify the graph boundary type for $y\le -x+3$: solid line or dashed line?
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Solid line. Non-strict inequalities ($\le$ or $\ge$) use solid boundaries.
Solid line. Non-strict inequalities ($\le$ or $\ge$) use solid boundaries.
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Identify the graph boundary type for $y>2x-1$: solid line or dashed line?
Identify the graph boundary type for $y>2x-1$: solid line or dashed line?
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Dashed line. Strict inequalities ($>$ or $<$) use dashed boundaries.
Dashed line. Strict inequalities ($>$ or $<$) use dashed boundaries.
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What is the interval notation for $-2<x\le 4$?
What is the interval notation for $-2<x\le 4$?
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$(-2,4]$. Parenthesis excludes -2, bracket includes 4.
$(-2,4]$. Parenthesis excludes -2, bracket includes 4.
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What is the interval notation for $x\le -1$?
What is the interval notation for $x\le -1$?
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$(-\infty,-1]$. Bracket includes -1; negative infinity uses parenthesis.
$(-\infty,-1]$. Bracket includes -1; negative infinity uses parenthesis.
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What is the interval notation for $x<-1$?
What is the interval notation for $x<-1$?
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$(-\infty,-1)$. Parenthesis excludes -1; negative infinity uses parenthesis.
$(-\infty,-1)$. Parenthesis excludes -1; negative infinity uses parenthesis.
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What is the interval notation for $x>5$?
What is the interval notation for $x>5$?
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$(5,\infty)$. Parenthesis excludes 5; infinity always uses parenthesis.
$(5,\infty)$. Parenthesis excludes 5; infinity always uses parenthesis.
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What is the solution set meaning of $x\le -2$ on a number line?
What is the solution set meaning of $x\le -2$ on a number line?
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All real numbers less than or equal to $-2$. Closed circle at -2, shading extends leftward infinitely.
All real numbers less than or equal to $-2$. Closed circle at -2, shading extends leftward infinitely.
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What is the solution set meaning of $x>3$ on a number line?
What is the solution set meaning of $x>3$ on a number line?
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All real numbers greater than $3$. Open circle at 3, shading extends rightward infinitely.
All real numbers greater than $3$. Open circle at 3, shading extends rightward infinitely.
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What is the solution to the inequality $\frac{x-2}{3}<4$?
What is the solution to the inequality $\frac{x-2}{3}<4$?
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$x<14$. Multiply by 3, then add 2: $x - 2 < 12$.
$x<14$. Multiply by 3, then add 2: $x - 2 < 12$.
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Identify the solution to $\frac{x-1}{-2}\le 3$.
Identify the solution to $\frac{x-1}{-2}\le 3$.
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$x\ge -5$. Multiply by $-2$ (flip sign), then add $1$.
$x\ge -5$. Multiply by $-2$ (flip sign), then add $1$.
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Identify the solution: Solve $\frac{x}{4} \ge -3$.
Identify the solution: Solve $\frac{x}{4} \ge -3$.
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$x \ge -12$. Multiply both sides by 4.
$x \ge -12$. Multiply both sides by 4.
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What does the phrase "no more than" translate to in an inequality?
What does the phrase "no more than" translate to in an inequality?
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$\le$. "No more than" sets a maximum, so less than or equal to.
$\le$. "No more than" sets a maximum, so less than or equal to.
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What does the word "at least" translate to in an inequality?
What does the word "at least" translate to in an inequality?
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$\ge$. "At least" means the minimum value, so greater than or equal to.
$\ge$. "At least" means the minimum value, so greater than or equal to.
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What inequality symbol results after dividing both sides by a negative number?
What inequality symbol results after dividing both sides by a negative number?
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Reverse the inequality: $\le$ becomes $\ge$ and vice versa. Negative operations flip inequality signs to maintain truth.
Reverse the inequality: $\le$ becomes $\ge$ and vice versa. Negative operations flip inequality signs to maintain truth.
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Identify the solution: Solve $5-\frac{x}{2} < 1$.
Identify the solution: Solve $5-\frac{x}{2} < 1$.
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$x > 8$. Subtract 5: $-\frac{x}{2} < -4$, multiply by -2 and flip.
$x > 8$. Subtract 5: $-\frac{x}{2} < -4$, multiply by -2 and flip.
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What interval notation corresponds to $-2 < x \le 5$?
What interval notation corresponds to $-2 < x \le 5$?
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$(-2,5]$. Parenthesis excludes -2; square bracket includes 5.
$(-2,5]$. Parenthesis excludes -2; square bracket includes 5.
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What interval notation corresponds to $x \ge 3$?
What interval notation corresponds to $x \ge 3$?
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$[3,\infty)$. Square bracket includes 3; infinity is always with parenthesis.
$[3,\infty)$. Square bracket includes 3; infinity is always with parenthesis.
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What is the graph symbol for $x \ge a$ on a number line?
What is the graph symbol for $x \ge a$ on a number line?
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Closed circle at $a$; shade to the right. Closed circle includes the endpoint; shade shows valid values.
Closed circle at $a$; shade to the right. Closed circle includes the endpoint; shade shows valid values.
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What is the graph symbol for $x > a$ on a number line?
What is the graph symbol for $x > a$ on a number line?
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Open circle at $a$; shade to the right. Open circle excludes the endpoint; shade shows valid values.
Open circle at $a$; shade to the right. Open circle excludes the endpoint; shade shows valid values.
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What is the graph symbol for $x \le a$ on a number line?
What is the graph symbol for $x \le a$ on a number line?
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Closed circle at $a$; shade to the left. Closed circle includes the endpoint; shade shows valid values.
Closed circle at $a$; shade to the left. Closed circle includes the endpoint; shade shows valid values.
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