How many integers x with -5 x 5 satisfy x + 2/x - 3 > 0?

Worked solution for TMUA-P1-MM1-018 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM1-018 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM1-018 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM1-018?

No — calculators are banned in the TMUA. TMUA-P1-MM1-018 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM1-018?

TMUA-P1-MM1-018 is Paper P1 · Algebra and functions (specification code MM1), level 3. Drill more of the same topic from this page.

TMUA-P1-MM1-018 — Paper P1 · Algebra and functions · Level 3

P1MM1Level 3~240s target

Spec: MM1 · No calculator · ~240s

How many integers

x

with

-5 \le x \le 5

satisfy

\dfrac{x + 2}{x - 3} > 0

Options

$5$
$6$
$7$
$8$
$11$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: rational-inequality, zero-denominator. Name the trap first, work the stem by hand, then open the solution below.

Show solution

The fraction is positive when numerator and denominator share a sign:

x < -2

x > 3

. In

[-5, 5]

that gives

\{-5,-4,-3,4,5\}

5

integers. Trap:

7

includes

x = -2

(numerator zero, fraction equals

0

) and

x = 3

(division by zero) — both fail the strict inequality.

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Same topic · same level

P1MM1Level 3

TMUA-P1-MM1-016

The polynomial P(x) = x^3 + px^2 + qx - 12 is divisible by both (x - 1) and (x + 3). What is the value of p?

Algebra and functions

Open TMUA-P1-MM1-016 →

TMUA-P1-MM1-018 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

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TMUA-P1-MM1-018 — Paper P1 · Algebra and functions · Level 3

Options

Keep practising

Master Algebra and functions