Solve Two-Step Linear Equations - 7th Grade Math
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What is the number if $ rac{3}{5}$ of a number, then add 2, gives 11?
What is the number if $ rac{3}{5}$ of a number, then add 2, gives 11?
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$x=15$. Set up $ rac{3}{5}x+2=11$, solve: $x=15$.
$x=15$. Set up $ rac{3}{5}x+2=11$, solve: $x=15$.
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What is the first inverse operation to isolate $x$ in an equation of the form $px+q=r$?
What is the first inverse operation to isolate $x$ in an equation of the form $px+q=r$?
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Subtract $q$ from both sides. This reverses the addition of $q$ to begin isolating $x$.
Subtract $q$ from both sides. This reverses the addition of $q$ to begin isolating $x$.
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What is the second inverse operation to isolate $x$ in an equation of the form $px+q=r$ after subtracting $q$?
What is the second inverse operation to isolate $x$ in an equation of the form $px+q=r$ after subtracting $q$?
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Divide both sides by $p$. This reverses the multiplication by $p$ to solve for $x$.
Divide both sides by $p$. This reverses the multiplication by $p$ to solve for $x$.
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What is the first step to isolate $x$ in an equation of the form $p(x+q)=r$?
What is the first step to isolate $x$ in an equation of the form $p(x+q)=r$?
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Divide both sides by $p$. This removes the coefficient $p$ from the parentheses.
Divide both sides by $p$. This removes the coefficient $p$ from the parentheses.
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What is the second step to isolate $x$ in an equation of the form $p(x+q)=r$ after dividing by $p$?
What is the second step to isolate $x$ in an equation of the form $p(x+q)=r$ after dividing by $p$?
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Subtract $q$ from both sides. This isolates $x$ after the parentheses are removed.
Subtract $q$ from both sides. This isolates $x$ after the parentheses are removed.
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What is the distributive property rewrite of $p(x+q)$?
What is the distributive property rewrite of $p(x+q)$?
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$p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.
$p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.
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What is the arithmetic meaning of $px+q=r$ in a word problem?
What is the arithmetic meaning of $px+q=r$ in a word problem?
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A number times $p$, then add $q$, equals $r$. Multiply unknown by $p$, add $q$ to get $r$.
A number times $p$, then add $q$, equals $r$. Multiply unknown by $p$, add $q$ to get $r$.
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What is the arithmetic meaning of $p(x+q)=r$ in a word problem?
What is the arithmetic meaning of $p(x+q)=r$ in a word problem?
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Add $q$ to a number, then multiply by $p$ to get $r$. First add $q$ to unknown, then multiply result by $p$.
Add $q$ to a number, then multiply by $p$ to get $r$. First add $q$ to unknown, then multiply result by $p$.
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Identify the equation that matches: “$3$ more than twice a number is $17$.”
Identify the equation that matches: “$3$ more than twice a number is $17$.”
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$2x+3=17$. "Twice a number" is $2x$, "3 more" adds 3.
$2x+3=17$. "Twice a number" is $2x$, "3 more" adds 3.
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Identify the equation that matches: “Five times the sum of a number and $4$ is $35$.”
Identify the equation that matches: “Five times the sum of a number and $4$ is $35$.”
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$5(x+4)=35$. "Sum of a number and 4" is $(x+4)$, times 5.
$5(x+4)=35$. "Sum of a number and 4" is $(x+4)$, times 5.
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What is $x$ if $-3x+5=-10$?
What is $x$ if $-3x+5=-10$?
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$x=5$. Subtract 5: $-3x=-15$, then divide by -3.
$x=5$. Subtract 5: $-3x=-15$, then divide by -3.
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What is $x$ if $ rac{1}{2}x+3=7$?
What is $x$ if $ rac{1}{2}x+3=7$?
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$x=8$. Subtract 3: $ rac{1}{2}x=4$, then multiply by 2.
$x=8$. Subtract 3: $ rac{1}{2}x=4$, then multiply by 2.
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What is $x$ if $0.2x+1=3$?
What is $x$ if $0.2x+1=3$?
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$x=10$. Subtract 1: $0.2x=2$, then divide by 0.2.
$x=10$. Subtract 1: $0.2x=2$, then divide by 0.2.
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What is $x$ if $6(x-2)=24$?
What is $x$ if $6(x-2)=24$?
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$x=6$. Divide by 6: $x-2=4$, then add 2.
$x=6$. Divide by 6: $x-2=4$, then add 2.
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What is $x$ if $- rac{3}{4}(x+8)=6$?
What is $x$ if $- rac{3}{4}(x+8)=6$?
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$x=-16$. Divide by $- rac{3}{4}$: $x+8=-8$, then subtract 8.
$x=-16$. Divide by $- rac{3}{4}$: $x+8=-8$, then subtract 8.
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What is $x$ if $ rac{2}{3}(x-9)=-4$?
What is $x$ if $ rac{2}{3}(x-9)=-4$?
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$x=3$. Divide by $ rac{2}{3}$: $x-9=-6$, then add 9.
$x=3$. Divide by $ rac{2}{3}$: $x-9=-6$, then add 9.
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What is $x$ if $-2(x+5)=14$?
What is $x$ if $-2(x+5)=14$?
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$x=-12$. Divide by -2: $x+5=-7$, then subtract 5.
$x=-12$. Divide by -2: $x+5=-7$, then subtract 5.
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What is the number if “Subtract $4$, then multiply by $3$, to get $18$”?
What is the number if “Subtract $4$, then multiply by $3$, to get $18$”?
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$x=10$. Set up $3(x-4)=18$, solve: $x=10$.
$x=10$. Set up $3(x-4)=18$, solve: $x=10$.
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Which form matches: “A gym charges a $12$ fee plus $5$ dollars per class for $c$ classes”?
Which form matches: “A gym charges a $12$ fee plus $5$ dollars per class for $c$ classes”?
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$5c+12=r$. Fixed fee $12$ plus variable cost $5c$ equals total $r$.
$5c+12=r$. Fixed fee $12$ plus variable cost $5c$ equals total $r$.
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What is $x$ if you buy $x$ notebooks at $\$2$ each, use a $$5$ coupon, and pay $\$13$?
What is $x$ if you buy $x$ notebooks at $\$2$ each, use a $$5$ coupon, and pay $\$13$?
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$x=9$. Solve $2x-5=13$: add 5, divide by 2.
$x=9$. Solve $2x-5=13$: add 5, divide by 2.
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What equation matches: “You buy $x$ notebooks at $\$2$ each and use a $$5$ coupon; you pay $\$13$.”
What equation matches: “You buy $x$ notebooks at $\$2$ each and use a $$5$ coupon; you pay $\$13$.”
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$2x-5=13$. Total cost minus coupon discount equals amount paid.
$2x-5=13$. Total cost minus coupon discount equals amount paid.
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What is the first inverse operation to isolate $x$ in an equation of the form $p(x+q)=r$?
What is the first inverse operation to isolate $x$ in an equation of the form $p(x+q)=r$?
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Divide both sides by $p$. This removes the parentheses and isolates the $(x+q)$ term.
Divide both sides by $p$. This removes the parentheses and isolates the $(x+q)$ term.
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What is the distributive property for expanding $p(x+q)$?
What is the distributive property for expanding $p(x+q)$?
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$p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.
$p(x+q)=px+pq$. Multiply $p$ by each term inside the parentheses.
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What is the equation form for “$q$ more than $p$ times a number is $r$”?
What is the equation form for “$q$ more than $p$ times a number is $r$”?
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$px+q=r$. "More than" means addition after multiplication.
$px+q=r$. "More than" means addition after multiplication.
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What is the equation form for “$p$ times the sum of a number and $q$ is $r$”?
What is the equation form for “$p$ times the sum of a number and $q$ is $r$”?
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$p(x+q)=r$. "Times the sum" means multiply the entire addition.
$p(x+q)=r$. "Times the sum" means multiply the entire addition.
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