SAT-93: The Extreme Plug-In Technique (0, 1, Negatives)

SAT-93: The Extreme Plug-In Technique (0, 1, Negatives)

Description: Plugging in (SAT-81) gets even more powerful when you choose extreme values on purpose — 0, 1, and negatives. These special numbers behave in unusual ways and quickly expose which answer choices are wrong, especially on "which expression is always true?" questions.

Why extremes are powerful

• 0 makes many terms vanish, simplifying instantly.
• 1 is the multiplicative identity, so it isolates the structure.
• Negatives reveal sign mistakes that positive numbers hide.

(Oʻzbekcha: 0, 1 va manfiy sonlar koʻp hadlarni soddalashtiradi va ishora xatolarini ochib beradi.)

The caution

Use extremes for eliminating, but be aware: 0 and 1 can occasionally make two choices look equal. If that happens, switch to a different extreme (like −2) to break the tie. (Oʻzbekcha: 0 va 1 baʼzan ikki variantni teng koʻrsatadi — bunday holatda −2 kabi boshqa qiymatni sinang.)

Worked Example 1 — eliminate with 0

Which equals 0 when x = 0? (A) x + 1 (B) x² (C) 2x − 3 (D) (x − 1).

• Plug x = 0: (A) 1, (B) 0, (C) −3, (D) −1. Only (B) gives 0 → (B).

Worked Example 2 — "always true" question

Which is always equal to 2(x + 3)? (A) 2x + 3 (B) 2x + 6 (C) x + 6 (D) 2x + 5.

• Test x = 0: target 2(3) = 6. Choices give (A) 3, (B) 6, (C) 6, (D) 5. (B) and (C) tie.
• Break the tie with x = 1: target 2(4) = 8. (B) 2+6 = 8 ✓; (C) 1+6 = 7 ✗. Answer (B).

(Oʻzbekcha: ikki variant teng chiqsa, x = 1 bilan farqlang.)

Worked Example 3 — catch a sign error with a negative

Is |x| = x always true? Test x = −3.

• |−3| = 3 but x = −3, so 3 ≠ −3. The statement is false — the negative exposed it instantly.
• (A positive test value like x = 3 would have wrongly suggested it's true.)

Worked Example 4 — fractions with 1

Which equals 1 when x = 1? (A) x/2 (B) 2x (C) x² (D) x + 1.

• Plug x = 1: (A) 0.5, (B) 2, (C) 1, (D) 2. Only (C) gives 1 → (C).

Tip: when a question says "for all x" or "always," extreme plug-ins are the fastest way to kill wrong choices. (Oʻzbekcha: "barcha x uchun" deyilsa, ekstremal qiymatlar eng tez yoʻl.)

Which extreme to reach for first

A quick decision guide: try 0 first on most "always equal" questions, since it instantly zeroes out many terms and is the fastest to compute. If 0 leaves two choices tied, jump to 1, which separates expressions that differ by a coefficient. Save a negative for any question involving absolute value, squaring, or inequalities, where sign behavior is the whole point. Cycling through 0, then 1, then a negative will resolve almost every elimination question without algebra. (Oʻzbekcha: avval 0 ni, keyin 1 ni, soʻng manfiyni sinang — shu tartibda koʻp savol hal boʻladi.)

Practice 1

Which expression equals 0 when x = 0? (A) x − 2 (B) 3x (C) x + 5 (D) x² + 1.

Practice 2

Test whether (x + 2)² = x² + 4 for all x by trying x = 1.

Key words — Kalit soʻzlar

• Extreme value — ekstremal qiymat
• Zero — nol
• Identity (1) — birlik (1)
• Negative — manfiy
• Always true — har doim toʻgʻri
• Eliminate — chiqarib tashlash
• Absolute value — modul (absolyut qiymat)
• Break the tie — tenglikni buzish
• Sign error — ishora xatosi

Summary

• Test 0, 1, and negatives to expose wrong choices quickly.
• 0 simplifies, 1 isolates structure, negatives catch sign errors.
• If two choices tie, switch to another extreme to break it.