Solve and Graph Linear Inequalities - 7th Grade Math
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What is the solution to $m-7.5<12$?
What is the solution to $m-7.5<12$?
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$m<19.5$. Add 7.5 to both sides: $m<12+7.5=19.5$.
$m<19.5$. Add 7.5 to both sides: $m<12+7.5=19.5$.
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What is the graph description for $x<-2$: circle type and shading direction?
What is the graph description for $x<-2$: circle type and shading direction?
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Open circle at $-2$, shade left. For $x<-2$, exclude -2 (open circle) and shade values less than -2.
Open circle at $-2$, shade left. For $x<-2$, exclude -2 (open circle) and shade values less than -2.
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What inequality represents: “After spending $7.50$, you have less than $12$ left from $m$ dollars”?
What inequality represents: “After spending $7.50$, you have less than $12$ left from $m$ dollars”?
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$m-7.5<12$. Starting amount minus spending must be less than 12.
$m-7.5<12$. Starting amount minus spending must be less than 12.
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Which value satisfies $4x+1<9$: $x=1$ or $x=3$?
Which value satisfies $4x+1<9$: $x=1$ or $x=3$?
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$x=1$. Test: $4(1)+1=5<9$ ✓; $4(3)+1=13>9$ ✗.
$x=1$. Test: $4(1)+1=5<9$ ✓; $4(3)+1=13>9$ ✗.
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What inequality represents: “You need more than $60$ points; you already have $18$ and earn $6$ per game $g$”?
What inequality represents: “You need more than $60$ points; you already have $18$ and earn $6$ per game $g$”?
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$18+6g>60$. Current points plus points per game must exceed 60.
$18+6g>60$. Current points plus points per game must exceed 60.
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What is the solution for games $g$ in $18+6g>60$?
What is the solution for games $g$ in $18+6g>60$?
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$g>7$. Subtract 18, divide by 6: $6g>42$, so $g>7$.
$g>7$. Subtract 18, divide by 6: $6g>42$, so $g>7$.
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What is the solution to the inequality $- rac{3}{4}x-2<1$?
What is the solution to the inequality $- rac{3}{4}x-2<1$?
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$x>-4$. Add 2, divide by $- rac{3}{4}$ (flip sign): $- rac{3}{4}x<3$, so $x>-4$.
$x>-4$. Add 2, divide by $- rac{3}{4}$ (flip sign): $- rac{3}{4}x<3$, so $x>-4$.
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What is the solution to the inequality $ rac{1}{2}x+3<7$?
What is the solution to the inequality $ rac{1}{2}x+3<7$?
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$x<8$. Subtract 3, multiply by 2: $ rac{1}{2}x<4$, so $x<8$.
$x<8$. Subtract 3, multiply by 2: $ rac{1}{2}x<4$, so $x<8$.
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What inequality represents: “Three times a number $x$ decreased by $2$ is less than $10$”?
What inequality represents: “Three times a number $x$ decreased by $2$ is less than $10$”?
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$3x-2<10$. "Times" means multiply; "decreased by" means subtract; "less than" gives $<$.
$3x-2<10$. "Times" means multiply; "decreased by" means subtract; "less than" gives $<$.
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What inequality represents: “A number $x$ increased by $5$ is greater than $12$”?
What inequality represents: “A number $x$ increased by $5$ is greater than $12$”?
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$x+5>12$. "Increased by" means addition; "greater than" gives $>$.
$x+5>12$. "Increased by" means addition; "greater than" gives $>$.
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What inequality represents: “The cost is a $10$ dollar fee plus $2.5$ dollars per hour $h$, under $40$”?
What inequality represents: “The cost is a $10$ dollar fee plus $2.5$ dollars per hour $h$, under $40$”?
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$10+2.5h<40$. Fixed fee plus hourly rate must be under the limit.
$10+2.5h<40$. Fixed fee plus hourly rate must be under the limit.
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What is the solution for hours $h$ in $10+2.5h<40$?
What is the solution for hours $h$ in $10+2.5h<40$?
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$h<12$. Subtract 10, divide by 2.5: $2.5h<30$, so $h<12$.
$h<12$. Subtract 10, divide by 2.5: $2.5h<30$, so $h<12$.
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What is the solution to the inequality $-2x+1>9$?
What is the solution to the inequality $-2x+1>9$?
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$x<-4$. Subtract 1, divide by -2 (flip sign): $-2x>8$, so $x<-4$.
$x<-4$. Subtract 1, divide by -2 (flip sign): $-2x>8$, so $x<-4$.
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Which graph shows a strict inequality, $x>3$ or $x<3$: open circle or closed circle?
Which graph shows a strict inequality, $x>3$ or $x<3$: open circle or closed circle?
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Open circle. Open circles exclude the boundary value in strict inequalities.
Open circle. Open circles exclude the boundary value in strict inequalities.
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What must you do to an inequality sign when you multiply or divide by a negative number?
What must you do to an inequality sign when you multiply or divide by a negative number?
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Reverse the sign: $>$ becomes $<$ and $<$ becomes $>$. Multiplying/dividing by negatives flips the inequality direction.
Reverse the sign: $>$ becomes $<$ and $<$ becomes $>$. Multiplying/dividing by negatives flips the inequality direction.
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What inequality symbol means “less than” when translating a word problem?
What inequality symbol means “less than” when translating a word problem?
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$<$. The symbol $<$ indicates one value is smaller than another.
$<$. The symbol $<$ indicates one value is smaller than another.
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What inequality symbol means “greater than” when translating a word problem?
What inequality symbol means “greater than” when translating a word problem?
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$>$. The symbol $>$ indicates one value exceeds another.
$>$. The symbol $>$ indicates one value exceeds another.
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What does the solution set of an inequality represent in a word problem context?
What does the solution set of an inequality represent in a word problem context?
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All values of $x$ that make the situation true. The solution set includes all possible values that satisfy the inequality.
All values of $x$ that make the situation true. The solution set includes all possible values that satisfy the inequality.
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What does the inequality symbol $<$ mean in a word problem?
What does the inequality symbol $<$ mean in a word problem?
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$<$ means “less than.”. This symbol indicates one value is smaller than another.
$<$ means “less than.”. This symbol indicates one value is smaller than another.
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What does the inequality symbol $>$ mean in a word problem?
What does the inequality symbol $>$ mean in a word problem?
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$>$ means “greater than.”. This symbol indicates one value is larger than another.
$>$ means “greater than.”. This symbol indicates one value is larger than another.
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What inequality represents: “A number $x$ increased by $5$ is more than $12$”?
What inequality represents: “A number $x$ increased by $5$ is more than $12$”?
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$x+5>12$. "Increased by" means addition; "more than" means $>$.
$x+5>12$. "Increased by" means addition; "more than" means $>$.
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Identify the solution: Solve $-2x+1>9$.
Identify the solution: Solve $-2x+1>9$.
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$x<-4$. Subtract $1$, divide by $-2$, and flip the sign: $-2x>8$.
$x<-4$. Subtract $1$, divide by $-2$, and flip the sign: $-2x>8$.
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Identify the solution: Solve $5x-7<8$.
Identify the solution: Solve $5x-7<8$.
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$x<3$. Add $7$, then divide by $5$: $5x<15$.
$x<3$. Add $7$, then divide by $5$: $5x<15$.
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What inequality represents: “You have $20$ dollars and spend $3x$; you want more than $5$ left”?
What inequality represents: “You have $20$ dollars and spend $3x$; you want more than $5$ left”?
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$20-3x>5$. Money left is $20-3x$; "more than $5$" means $>5$.
$20-3x>5$. Money left is $20-3x$; "more than $5$" means $>5$.
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Identify the solution: Solve $3x+2>11$.
Identify the solution: Solve $3x+2>11$.
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$x>3$. Subtract $2$, then divide by $3$: $3x>9$.
$x>3$. Subtract $2$, then divide by $3$: $3x>9$.
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