Silly mistake

An SAT micro-topic explainer. Free to read — no account needed.

On a hard test, many errors are not about not knowing the maths — they are silly mistakes made in a hurry.
Knowing the common traps helps you catch them before they cost a mark.
silly_mistake_checklist.png
The most frequent slip is answering the wrong quantity.
If you solve 2x=102x = 10 to get x=5x = 5 but the question asks for x+1x + 1, the answer is 66, not 55.
Always check what the question actually wants before choosing.
Sign and distribution errors are the next most common.
Dropping a minus turns −(x−5)-(x - 5) into −x−5-x - 5 instead of the correct −x+5-x + 5.
Distribute across the whole bracket and keep track of every negative as you go.
So the fix is a quick habit: solve, then re-read and sanity-check.
Confirm the answer matches the quantity asked, the sign is right, and the size is reasonable.
A few seconds of checking saves marks that were never really in doubt.

Worked examples

Solve 3x=123x = 12, then give the value of x+4x + 4.
(A) 44
(B) 88
Solving gives x=4x = 4, but the question asks for x+4x + 4, not xx.
So the answer is 4+4=84 + 4 = 8, which is (B); choosing (A) is the silly-mistake trap.
Simplify −(x−3)+2x-(x - 3) + 2x.
(A) x+3x + 3
(B) 3x−33x - 3
Distributing the minus gives −x+3-x + 3, so −x+3+2x=x+3-x + 3 + 2x = x + 3.
Dropping the sign would wrongly give 3x−33x - 3, so the correct answer is (A).
A rectangle is xx cm wide and twice as long. If x=5x = 5, what is its perimeter?
(A) 1515
(B) 3030
The length is 1010, so the perimeter is 2(5)+2(10)=302(5) + 2(10) = 30; answering 1515 would come from forgetting to double or from finding just half.
So the correct answer is (B).

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