ARCH-M1-08: Simultaneous Linear Combinations, Straight-Line Gradients & Inequalities

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-M1-08: Why the 135s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~135s (Blows 90s Clock)

Subtract

7

from both sides:

-\frac{3x}{2} > 6

. Multiply both sides by

2

-3x > 12

. Dividing both sides by

-3

reverses the inequality sign, giving

x < -4

(~85s).

The Fast ShortcutTarget: 35s (Saves 100s)

**Line 1 (Move

-\frac{3x}{2}

to Positive Side):**

7 - 13 > \frac{3x}{2} \implies -6 > \frac{3x}{2}

.
**Line 2 (Scale by

\frac{2}{3}

):**

-4 > x \implies x < -4

(20s).

Where Students Lose Time: In 23 past UAT-UK questions (10.22% of Mathematics 1), candidates lose 100s by keeping the inequality direction unchanged when dividing by -a. Instead, apply M4 with Maths 1 skill M4.6.

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