Practice
Writing Equations Practice
Fifty original questions covering the complete writing equations lesson, with explanations and SAT-focused strategy.
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Question 1
Explanation
This tests equation vocabulary. An equation uses an equal sign to assert that two complete expressions have the same value. A variable expression without an equality claim is not an equation.
Question 2
Explanation
The skill is interpreting equality. The sign states that the value of \(7x-2\) is the same as \(19\) for any solution. It does not specify an order of calculation.
Question 3
Explanation
‘Added to’ signals addition, so the left side is \(x+8\). The word ‘equals’ supplies the equality with \(23\), giving \(x+8=23\).
Question 4
Explanation
‘Five times \(n\)’ is the product \(5n\), and ‘is’ means equality. Therefore the complete equation is \(5n=45\).
Question 5
Explanation
The original quantity is \(p\). Decreasing it by \(7\) gives \(p-7\), and ‘is \(12\)’ completes \(p-7=12\). Reversing the subtraction changes the relationship.
Question 6
Explanation
Four more than \(y\) means add \(4\) to \(y\), producing \(y+4\). The equality phrase produces \(y+4=18\).
Question 7
Explanation
‘Six less than \(t\)’ means six is subtracted from \(t\), so the left side is \(t-6\). Thus \(t-6=30\). Choice A is the classic reversed-order distractor.
Question 8
Explanation
The quotient of the first named quantity and the second is \(r\div3=r/3\). Joining it to \(9\) gives \(r/3=9\). Division order must be preserved.
Question 9
Explanation
Half of \(q\) is \(\frac12q=q/2\). The word ‘is’ connects that expression to \(11\), so \(q/2=11\).
Question 10
Explanation
A sum is addition, so the named quantity is \(a+b\). The equality word produces \(a+b=20\). This equation relates two variables without requiring either to be solved yet.
Question 11
Explanation
‘Is identical to’ signals equality, and the product of \(4\) and \(m\) is \(4m\). Therefore \(z=4m\).
Question 12
Explanation
An equation contains an equal sign and makes an equality claim. Only \(5y-1=24\) does so; the other choices merely name quantities.
Question 13
Explanation
A useful definition states the exact unknown quantity and, when relevant, its unit. ‘Let \(p\) be the number of pages Priya reads’ makes every later term interpretable.
Question 14
Explanation
‘Increased by’ adds \(13\) to \(k\), while ‘is the same as’ supplies equality. The result is \(k+13=31\).
Question 15
Explanation
‘The difference of \(x\) and \(9\)’ preserves the named order: \(x-9\). The equation is \(x-9=4\).
Question 16
Explanation
First form the complete sum \(x+6\), then multiply that grouped quantity by \(2\). The correct setup is \(2(x+6)=40\); \(2x+6\) fails to double the \(6\).
Question 17
Explanation
The difference is \(n-5\). One-third of that whole difference is \((n-5)/3\), so the equation is \((n-5)/3=7\). The fraction bar groups the numerator.
Question 18
Explanation
Three times \(x\) is \(3x\), and five more gives \(3x+5\). That complete quantity equals \(x+19\), producing \(3x+5=x+19\).
Question 19
Explanation
The wording first creates twice \(x\), or \(2x\), and then decreases that result by \(7\). Thus \(2x-7=y\). Parentheses would mean \(x\) is decreased before doubling.
Question 20
Explanation
The quotient is \(p/4\). Twelve less than that quotient means subtract \(12\) from it, giving \(p/4-12=9\).
Question 21
Explanation
The monthly cost is \(8m\), while the one-time joining fee is added once. The total model is \(8m+12=44\). Choice A incorrectly repeats the joining fee each month.
Question 22
Explanation
The mileage charge is \(1.80d\) dollars, and the fixed \(4.50\)-dollar charge is added once. Therefore \(C=1.80d+4.50\).
Question 23
Explanation
The width is the smaller quantity: start with the length and subtract \(5\). Thus \(w=L-5\). Testing \(L=20\) gives the sensible width \(15\).
Question 24
Explanation
The adult price is the student price plus \(3\), so \(a=s+3\). Choice B would make the student ticket more expensive.
Question 25
Explanation
First form the complete difference \(F-32\), then take five-ninths of it. This gives \(C=\frac59(F-32)\). Missing the parentheses changes which terms receive the factor.
Question 26
Explanation
Consecutive integers increase by \(1\), so the three values are \(n,n+1,n+2\). Their sum, not product, equals \(72\), giving \(n+(n+1)+(n+2)=72\).
Question 27
Explanation
Starting with the least integer \(k\), add \(1,2,3\) to obtain the next three integers. Adding them produces \(k+(k+1)+(k+2)+(k+3)=154\).
Question 28
Explanation
Consecutive even integers differ by \(2\), so the list is \(e,e+2,e+4\), with \(e\) even. Their sum gives \(e+(e+2)+(e+4)=96\).
Question 29
Explanation
Odd integers occur every two integers. Beginning with odd \(o\), the next values are \(o+2,o+4,o+6\). Their stated sum is \(160\).
Question 30
Explanation
Because \(g\) is the greatest, the earlier integers are \(g-1,g-2,g-3\). Their sum with \(g\) is \((g-3)+(g-2)+(g-1)+g=86\).
Question 31
Explanation
Adding \(2\) preserves parity but does not choose it. If \(n=4\), all terms are even; if \(n=5\), all are odd. The variable definition must supply the required parity.
Question 32
Explanation
An average is the entire sum divided by the number of values. There are three values, so \(\frac{x+y+12}{3}=20\). Grouping the numerator is essential.
Question 33
Explanation
The named difference is the complete quantity \(x-5\). Its product with \(2\) is \(2(x-5)\), so \(2(x-5)=18\).
Question 34
Explanation
One-half of \(c\) is \(c/2\). A quantity \(b\) less than that is \(c/2-b\), and this equals \(a\). Thus \(a=c/2-b\).
Question 35
Explanation
An increase of \(25\%\) of \(x\) adds \(0.25x\) to the original \(x\). The correct model is \(x+0.25x=90\), equivalently \(1.25x=90\).
Question 36
Explanation
The named sum is \(p+q\). Forty percent of the entire sum is \(0.40(p+q)\), which equals \(r\). Choices A and D apply the percent to only one term.
Question 37
Explanation
Rate times time gives \(rt\) produced pages. Discarding \(15\) from that total gives \(P=rt-15\). The units confirm that \(15\) is pages, not minutes or pages per minute.
Question 38
Explanation
The drained amount is rate times time, \(dm\) liters. Subtract it from the initial \(v\) liters: \(R=v-dm\). Grouping \((v-d)m\) would incorrectly multiply the initial amount by time.
Question 39
Explanation
A variable should represent a precise quantity, such as the number of homework problems or hours spent. ‘The homework’ gives neither a measurable value nor units, so equations using \(h\) would be ambiguous.
Question 40
Explanation
‘Seven less than three times \(n\)’ means subtract \(7\) from \(3n\), not subtract \(3n\) from \(7\). The correct equation is \(3n-7=20\).
Question 41
Explanation
The next even integer after \(e\) is \(e+2\). ‘Product’ requires multiplication, so the equation is \(e(e+2)=224\), with \(e\) even.
Question 42
Explanation
‘\(a\) is twice \(b\)’ gives \(a=2b\). ‘\(b\) is five less than \(c\)’ gives \(b=c-5\). Both equations preserve which quantity is larger.
Question 43
Explanation
Two-fifths applies to the complete sum, so \(u=\frac25(v+w)\). Seven less than \(z\) is \(z-7\), so the second relationship is \(u=z-7\).
Question 44
Explanation
If \(m\) is the middle of five consecutive integers, there are two values below and two above: \(m-2,m-1,m,m+1,m+2\). Their sum equals \(235\).
Question 45
Explanation
Perimeter is twice the sum of one length and one width. Substituting length \(2w+3\) gives \(2[w+(2w+3)]=54\). Choice A counts only half the boundary.
Question 46
Explanation
The correct translation is \(3(x+4)\). At \(x=0\), it equals \(12\), while the student's \(3x+4\) equals \(4\), immediately proving the forms are not equivalent.
Question 47
Explanation
The left side \(4(n-2)\) is four times the complete difference of \(n\) and \(2\). The right side \(3n+11\) is eleven more than three times \(n\). Choice B states both structures exactly.
Question 48
Explanation
Six consecutive integers beginning with \(n\) end at \(n+5\). The problem adds only the least and greatest, so the required equation is \(n+(n+5)=73\), not the sum of all six.
Question 49
Explanation
One-half of \(x+6\) is \((x+6)/2\); one-third of \(x-3\) is \((x-3)/3\). Their difference is \(Q=\frac{x+6}{2}-\frac{x-3}{3}\).
Question 50
Explanation
Each deposit is \(p+15\) dollars, and \(d\) such deposits contribute \(d(p+15)\). Adding that total to starting balance \(B\) gives \(E=B+d(p+15)\).
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Questions to review
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- Question 1Equation meaningEasy
- Question 2Equality languageEasy
- Question 3Direct translationEasy
- Question 4Multiplication languageEasy
- Question 5Subtraction languageEasy
- Question 6Addition languageEasy
- Question 7Less-than reversalEasy
- Question 8Division languageEasy
- Question 9Fractional quantitiesEasy
- Question 10Two-variable equationsEasy
- Question 11Equality synonymsEasy
- Question 12Equation recognitionEasy
- Question 13Variable definitionsEasy
- Question 14Equality synonymsEasy
- Question 15Subtraction orderEasy
- Question 16Grouped translationMedium
- Question 17Fractional groupingMedium
- Question 18Multi-part translationMedium
- Question 19Operation order in languageMedium
- Question 20Nested subtractionMedium
- Question 21Context modelingMedium
- Question 22Rate modelsMedium
- Question 23Geometric relationshipsMedium
- Question 24Two-variable relationshipsMedium
- Question 25Formula translationMedium
- Question 26Consecutive integersMedium
- Question 27Consecutive integersMedium
- Question 28Consecutive even integersMedium
- Question 29Consecutive odd integersMedium
- Question 30Variable definitionsMedium
- Question 31Parity conditionsMedium
- Question 32Average modelsMedium
- Question 33Grouped productsMedium
- Question 34Nested variable relationshipsMedium
- Question 35Percent equationsMedium
- Question 36Percent groupingMedium
- Question 37Multi-stage modelsMedium
- Question 38Rate modelsMedium
- Question 39Variable definitionsMedium
- Question 40Error analysisMedium
- Question 41Consecutive-number productsHard
- Question 42Multiple relationshipsHard
- Question 43Systems modelingHard
- Question 44Centered sequencesHard
- Question 45Geometry modelingHard
- Question 46Model auditingHard
- Question 47Reverse translationHard
- Question 48Selective sequence modelingHard
- Question 49Complex fractional translationHard
- Question 50Repeated-group modelsHard