Card 1 of 20
EasyStudy card 1
Prompt
What is a variable?
It is not the same as a coefficient.
Answer
A symbol representing a number whose value may be unknown or may change.
Example
In \(4x+1\), \(x\) is the variable.
MathChapter 1: The Language and Tools of Algebra
Flashcards
Variables and Expressions Flashcards
Twenty concise recall cards for variables and expressions, including rules, recognition, examples, traps, and SAT strategy.
Current card1 / 20
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is a constant term?
Ask what remains unchanged.
Answer
A term with no variable; its value is fixed.
Example
In \(7m-9\), \(-9\) is the constant term.
Card 3 of 20
EasyStudy card 3
Prompt
What is an algebraic expression?
An equation has an equals sign.
Answer
A combination of numbers, variables, operations, and grouping symbols without an equality claim.
Example
\(3(x-2)+5\) is an expression.
Card 4 of 20
EasyStudy card 4
Prompt
Translate ‘the sum of \(x\) and \(8\).’
‘Sum’ means addition.
Answer
\(x+8\)
Example
Order does not change this sum.
Card 5 of 20
MediumStudy card 5
Prompt
Translate ‘\(5\) less than \(x\).’
‘Less than’ reverses spoken order.
Answer
\(x-5\)
Example
For \(x=12\), the value is \(7\).
Card 6 of 20
MediumStudy card 6
Prompt
How does ‘\(5\) minus \(x\)’ differ from ‘\(5\) less than \(x\)’?
‘Minus’ preserves order.
Answer
It is \(5-x\), while ‘\(5\) less than \(x\)’ is \(x-5\).
Example
At \(x=8\), the values are \(-3\) and \(3\).
Card 7 of 20
EasyStudy card 7
Prompt
What does ‘product’ signal?
A coefficient beside a variable is a product.
Answer
Multiplication.
Example
The product of \(6\) and \(n\) is \(6n\).
Card 8 of 20
MediumStudy card 8
Prompt
What does ‘quotient of \(a\) and \(b\)’ mean?
The first named quantity is the numerator.
Answer
\(a/b\), with \(b\ne0\).
Example
The quotient of \(x+1\) and \(3\) is \((x+1)/3\).
Card 9 of 20
MediumStudy card 9
Prompt
Why group a multi-term numerator or divisor?
A fraction bar acts like grouping.
Answer
Grouping shows that the operation applies to the entire quantity.
Example
\(a/(b+2)\) divides by the whole sum.
Card 10 of 20
MediumStudy card 10
Prompt
Translate ‘twice the difference of \(x\) and \(3\).’
Build the difference first.
Answer
\(2(x-3)\)
Example
\(2x-3\) does not double the \(-3\).
Card 11 of 20
MediumStudy card 11
Prompt
What does a coefficient usually mean in a context?
Track units.
Answer
A per-unit rate or repeated amount multiplying the variable.
Example
In \(12n+5\), \(12\) can mean dollars per item.
Card 12 of 20
MediumStudy card 12
Prompt
What does a constant often mean in a context?
It is added once unless wording says otherwise.
Answer
A fixed amount that does not depend on the variable.
Example
In \(3m+7\), \(7\) can be a starting fee.
Card 13 of 20
MediumStudy card 13
Prompt
How should a negative value be substituted?
Protect the sign.
Answer
Place it in parentheses everywhere the variable appears.
Example
For \(x=-2\), write \(3(-2)^2\).
Card 14 of 20
MediumStudy card 14
Prompt
What units result from dollars per item times items?
Cancel the repeated unit.
Answer
Dollars.
Example
\((\text{dollars}/\text{item})(\text{items})=\text{dollars}\).
Card 15 of 20
MediumStudy card 15
Prompt
Translate ‘one-third of the sum \(a+6\).’
‘Of’ multiplies the whole named sum.
Answer
\((a+6)/3\)
Example
It can also be written \(\frac13(a+6)\).
Card 16 of 20
HardStudy card 16
Prompt
How do repeated addition and repeated multiplication differ?
One changes a coefficient; the other creates a power.
Answer
\(x+x+x=3x\), while \(x\cdot x\cdot x=x^3\).
Example
Do not replace \(3x\) with \(x^3\).
Card 17 of 20
MediumStudy card 17
Prompt
Translate ‘the average of \(x,y,10\).’
Average equals sum divided by count.
Answer
\((x+y+10)/3\)
Example
Group the entire sum in the numerator.
Card 18 of 20
HardStudy card 18
Prompt
What expression gives distance between \(x\) and \(7\)?
Distance cannot be negative.
Answer
\(|x-7|\)
Example
At \(x=2\), the distance is \(5\).
Card 19 of 20
MediumStudy card 19
Prompt
SAT check: how can easy numbers test a translation?
This detects reversed subtraction or division.
Answer
Substitute a simple value and compare it with the verbal situation.
Example
For ‘\(5\) less than \(12\),’ the result must be \(7\).
Card 20 of 20
HardStudy card 20
Prompt
What is the safest order for translating a nested phrase?
Work from noun phrase to modifier.
Answer
Build the innermost named quantity, group it, then apply each outer operation.
Example
‘Three times the sum’ becomes \(3(a+b)\).
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