In terms of means the answer should be written using a given variable or symbol. “Write the perimeter in terms of w” wants an expression with w, such as 4w + 10. “Solve for y in terms of x” means get y alone, with only x on the other side. “In terms of π” keeps π as a symbol: 9π, not 28.26.
In Spanish
en términos de
Also called
express in terms of, solve for y in terms of x, write in terms of, leave in terms of pi
In every case the answer keeps the named variable or symbol and gets the target quantity alone.
Formal definition and notation
To express a quantity Q in terms of a variable x is to write an equation Q = f(x) whose right side is an expression containing x (and constants) but not Q or any other unknown. To solve an equation for y in terms of x is to rearrange it into the form y = f(x) using inverse operations. “In terms of π” asks for an exact answer that keeps the irrational numberπ as a factor instead of a decimal approximation.
Symbol
Read it as
Meaning
y = f(x)
y equals an expression in x
the shape of an answer “for y in terms of x”
9π
nine pi
an exact answer “in terms of π“; about 28.27
Key facts
The variable after “in terms of” stays in the answer. It is not something to solve for.
“Solve for y in terms of x” is the same task as rewriting a line in slope-intercept form: 2x + 3y = 12 becomes y = −23x + 4.
“In terms of π” answers are exact; 3.14 or a calculator value is an approximation and is usually marked wrong on that question.
Tests often ask “in terms of” with a word problem: “If a pen costs p dollars, write the cost of 6 pens in terms of p” means 6p.
You may need to define a variable first. If the length is 5 more than the width w, then length = w + 5, and everything else follows in terms of w.
How to write an answer in terms of a variable
How to write an answer in terms of a variable
target = expression using only the given variable
target
the quantity the question names first (perimeter, y, cost, area)
given variable
the letter after “in terms of” (w, x, t, π); it stays in the answer
Check your answer: the target appears alone on one side, and the only letter on the other side is the given one. If a number replaced the variable, the question was misread.
“Solve for x” usually wants a number, as in 2x + 1 = 7, so x = 3. “In terms of” wants an expression that still contains a variable.
In Terms Ofvs.Evaluate
To evaluate is to substitute numbers and compute a single value. “In terms of” keeps the variable: evaluate 4w + 10 at w = 5 to get 30, but 4w + 10 itself is the answer in terms of w.
Quick check: 3 questions
Question 1 of 3
A square has side length s + 2. What is its area in terms of s?
Show answer and explanation
Answer: B. Area = (s + 2)2 = s2 + 4s + 4. s2 + 4 squares each part separately, 4s + 8 is the perimeter, and s2 + 2 forgets to square the 2.
Question 2 of 3
Solve x + 4y = 20 for x in terms of y.
Show answer and explanation
Answer: D. Subtract 4y from both sides: x = 20 − 4y. The first choice solves for y instead, 20 + 4y has the wrong sign, and 16y combines unlike terms.
Question 3 of 3
What is the circumference of a circle with diameter 10, in terms of π?
Show answer and explanation
Answer: A.C = π d = 10π. 31.4 is the decimal approximation (not in terms of π), 25π is the area, and 20π doubles the diameter as if it were the radius.
In Terms Of: frequently asked questions
What does "solve for y in terms of x" mean?
It means rearrange the equation so y is alone on one side and the other side uses only x and numbers. For 4x + 2y = 10, subtract 4x and divide by 2 to get y = 5 − 2x. The answer is a formula for y that works for every x, not a single number.
What does "in terms of pi" mean?
It means keep π as a symbol in the answer instead of replacing it with 3.14 or a calculator value. A circle with radius 6 has area 36π in terms of π. The answer is exact, and it is easy to approximate later: 36π ≈ 113.1.
Can the answer in terms of x be just a number?
Only if the variable cancels out. Usually the answer is an expression with x, such as 3x − 7. If you end up with only a number, check whether the question really asked to solve for x, or whether you substituted a value that was not given.
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