Inequality Showdown Warmup Handout
Algebra 1 PART 3: FRACTION & DECIMAL October 30, 2026
Stage 3: Mixed Representation Flip REGENTS PREP
October 30th Warm Up: Part 3 — The Fraction & Decimal Flip
Master the Algebraic Moves • Distribute, Cross the Line & CHANGE the Sign
AUGUST 2022 #21 (ADAPTED)
Name:
Date: October 30, 2026
Period:
1. Solve the linear inequality algebraically for x:
−1.5(2x − 4.8)
≤
5 2 x + 29.2
From NYS Regents Examination • Multi-Step Linear Inequalities with Mixed Numbers & Decimals
Step 1: Distribute decimals & write terms in the boxes and circles • Draw crossing arrows across the line!
Circle Team (Move Right • Change Sign!)
X-Box Team (Move Left • Change Sign!)
X-Box
Circle
≤
X-Box
Circle
+ Moved X-Box
≤
+ Moved Circle
Combined X-Box:
≤
Combined Circle:
≤ "Cross the Line... Change the Sign!" ≤
!
Final Step: Divide by Negative Coefficient!
Divide both sides by the coefficient! Because you divide by a negative number: You must flip the inequality symbol!
Final Solution: x
Symbol
Value
Number Line Plot:
Open Circle at _____
Solid Dot at _____
Ray: Left Right
−6
−5
−4
−3
−2
−1
0
TI-Nspire Check • Test a Value in Your Shaded Ray!
1. Store a test solution from your ray: → x • 2. Type: -1.5(2x - 4.8) ≤ (5/2)x + 29.2 • 3. Press ENTER → verify "true"!
Verified "TRUE"