Card 1 of 20
EasyStudy card 1
Prompt
What is an equation?
Look for an equality claim.
Answer
A mathematical statement that two expressions have the same value.
Example
\(3x+4=19\) is an equation; \(3x+4\) alone is an expression.
MathChapter 2: Solving Linear Equations
Flashcards
Writing Equations Flashcards
Twenty concise recall cards for writing equations, including rules, recognition, examples, traps, and SAT strategy.
Current card1 / 20
Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What does the equal sign mean?
It is a balance, not an instruction to calculate next.
Answer
The complete expressions on its two sides have equal value.
Example
\(A=B\) can also be written \(B=A\).
Card 3 of 20
EasyStudy card 3
Prompt
What makes a useful variable definition?
Define something measurable.
Answer
It names the exact unknown quantity and includes units when helpful.
Example
Let \(t\) be the travel time in hours.
Card 4 of 20
EasyStudy card 4
Prompt
Which words commonly signal equality?
They separate the two equal quantities.
Answer
‘Is,’ ‘equals,’ ‘is identical to,’ and ‘is the same as.’
Example
‘Twice \(n\) is \(14\)’ becomes \(2n=14\).
Card 5 of 20
MediumStudy card 5
Prompt
How is ‘\(7\) less than \(x\)’ translated?
‘Less than’ reverses the spoken order.
Answer
\(x-7\)
Example
At \(x=12\), seven less is \(5\).
Card 6 of 20
MediumStudy card 6
Prompt
How does ‘\(7\) minus \(x\)’ differ from ‘\(7\) less than \(x\)’?
‘Minus’ preserves order; ‘less than’ reverses it.
Answer
They are \(7-x\) and \(x-7\), respectively.
Example
At \(x=10\), the values are \(-3\) and \(3\).
Card 7 of 20
MediumStudy card 7
Prompt
Why does ‘twice the sum of \(x\) and \(5\)’ need parentheses?
Build the named sum before applying the outer operation.
Answer
Because \(2\) multiplies the complete sum: \(2(x+5)\).
Example
\(2x+5\) fails to double the \(5\).
Card 8 of 20
MediumStudy card 8
Prompt
How is ‘one-third of the difference \(n-4\)’ written?
A fraction bar groups its numerator.
Answer
\(\frac{n-4}{3}\)
Example
\(n/3-4\) applies one-third only to \(n\).
Card 9 of 20
MediumStudy card 9
Prompt
What is the safest order for writing an equation from words?
Separate modeling into deliberate stages.
Answer
Define the unknown, translate relationships, locate equality, then read the model back.
Example
Define \(m\) as months before writing a monthly-cost equation.
Card 10 of 20
EasyStudy card 10
Prompt
How are three consecutive integers beginning with \(n\) represented?
Ordinary consecutive integers differ by \(1\).
Answer
\(n,n+1,n+2\)
Example
Their sum is \(n+(n+1)+(n+2)\).
Card 11 of 20
MediumStudy card 11
Prompt
How are three consecutive even integers beginning with \(e\) represented?
Even integers occur two units apart.
Answer
\(e,e+2,e+4\), where \(e\) is even.
Example
If \(e=8\), the sequence is \(8,10,12\).
Card 12 of 20
MediumStudy card 12
Prompt
How are three consecutive odd integers beginning with \(o\) represented?
Odd integers also occur two units apart.
Answer
\(o,o+2,o+4\), where \(o\) is odd.
Example
If \(o=5\), the sequence is \(5,7,9\).
Card 13 of 20
HardStudy card 13
Prompt
Why does \(n,n+2,n+4\) not automatically mean even integers?
Check two possible starts.
Answer
The step preserves parity but does not determine whether the starting value is even or odd.
Example
Starting at \(4\) gives evens; starting at \(5\) gives odds.
Card 14 of 20
MediumStudy card 14
Prompt
If \(g\) is the greatest of four consecutive integers, how are all four represented?
Work backward from the defined greatest value.
Answer
\(g-3,g-2,g-1,g\)
Example
The sequence still increases by \(1\).
Card 15 of 20
MediumStudy card 15
Prompt
How is an average translated into an equation?
Average is total divided by count.
Answer
Divide the complete sum by the number of values, then set it equal to the stated average.
Example
The average of \(x,y,10\) being \(8\) gives \((x+y+10)/3=8\).
Card 16 of 20
MediumStudy card 16
Prompt
How should a fixed fee and a per-unit rate appear in a cost equation?
Use units to distinguish coefficient from constant.
Answer
Multiply the rate by the unit count and add the fixed fee once.
Example
At \(6\) dollars per visit plus \(10\) dollars fixed, \(C=6v+10\).
Card 17 of 20
HardStudy card 17
Prompt
What equation trap occurs when ‘increased by \(25\%\)’ is modeled as \(0.25x\)?
Include the original quantity.
Answer
That gives only the increase; the new amount is \(x+0.25x=1.25x\).
Example
A \(25\%\) increase on \(80\) gives \(100\), not \(20\).
Card 18 of 20
MediumStudy card 18
Prompt
How can units audit a verbal equation?
Track units beside each term.
Answer
Only quantities with compatible units may be added, and rate times count should produce the target unit.
Example
\((\text{dollars/item})(\text{items})=\text{dollars}\).
Card 19 of 20
HardStudy card 19
Prompt
How can a small test value detect reversed subtraction or missing grouping?
Zero and ten are often convenient.
Answer
Evaluate both the words and proposed expression at an easy value; any mismatch disproves the model.
Example
At \(x=0\), \(3(x+4)=12\) but \(3x+4=4\).
Card 20 of 20
HardStudy card 20
Prompt
Can an equation with two variables be a complete model without a unique numerical answer?
Modeling and solving are different tasks.
Answer
Yes. It may correctly state a relationship even when more information is needed to determine values.
Example
\(a=s+4\) fully states how two ticket prices relate.
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