Equation Enigma Worksheet
Algebra I • Equations Dual Self-Checking System
EQUATION ENIGMA
Name: Date:
Period: Score: / 8
1
Solve with Rigor
Show inverse operations in the workspace to isolate \(x\).
2
Substitution Check
Plug your answer into the check box. Prove LHS = RHS!
3
Mosaic Cipher
Match your answer in the Page 2 Key to reveal your color!
Part 1: Two-Step Equations (Problems 1–4)
Complete both the step-by-step work and the substitution verification.
# 1 \(4x - 7 = 17\) Two-Step
Step-by-Step Inverse Operations:
Solution: \(x =\)
Mosaic Color:
Substitution Verification Check: LHS = RHS
\(4(\,\underline{\hspace{18px}}\, ) - 7 \stackrel{?}{=} 17\) \(\rightarrow\) \(\underline{\hspace{18px}} - 7 = 17\) Verified
# 2 \(\frac{x}{2} + 9 = 7\) Two-Step
Step-by-Step Inverse Operations:
Solution: \(x =\)
Mosaic Color:
Substitution Verification Check: LHS = RHS
\(\frac{\underline{\hspace{18px}}}{2} + 9 \stackrel{?}{=} 7\) \(\rightarrow\) \(\underline{\hspace{18px}} + 9 = 7\) Verified
# 3 \(-5x + 7 = -8\) Two-Step
Step-by-Step Inverse Operations:
Solution: \(x =\)
Mosaic Color:
Substitution Verification Check: LHS = RHS
\(-5(\,\underline{\hspace{18px}}\, ) + 7 \stackrel{?}{=} -8\) \(\rightarrow\) \(\underline{\hspace{18px}} + 7 = -8\) Verified
# 4 \(\frac{2x + 1}{3} = 5\) Two-Step
Step-by-Step Inverse Operations:
Solution: \(x =\)
Mosaic Color:
Substitution Verification Check: LHS = RHS
\(\frac{2(\,\underline{\hspace{16px}}\, ) + 1}{3} \stackrel{?}{=} 5\) \(\rightarrow\) \(\frac{\underline{\hspace{18px}}}{3} = 5\) Verified
Self-Checking Equation Enigma • Master the Two-Step Foundation Continue to Multi-Step & Mystery Mosaic on Page 2
PART 2
Multi-Step Equations & Pattern Reveal
Name:
# 5 \(4(3x - 2) - 5x = 27\) Distribute & Combine
Show algebraic steps:
\(x =\)
Mosaic Color:
✓ Substitution Check: LHS \(\stackrel{?}{=}\) RHS
\(4(3(\underline{\hspace{10px}})-2) - 5(\underline{\hspace{10px}}) \stackrel{?}{=} 27\) \(27=27\)
# 6 \(6x + 5 = 2x + 21\) Variables Both Sides
Show algebraic steps:
\(x =\)
Mosaic Color:
✓ Substitution Check: LHS \(\stackrel{?}{=}\) RHS
\(6(\underline{\hspace{10px}}) + 5 \stackrel{?}{=} 2(\underline{\hspace{10px}}) + 21\) \(29=29\)
# 7 \(3(2x + 5) = x + 5\) Distribute & Balance
Show algebraic steps:
\(x =\)
Mosaic Color:
✓ Substitution Check: LHS \(\stackrel{?}{=}\) RHS
\(3(2(\underline{\hspace{10px}}) + 5) \stackrel{?}{=} (\underline{\hspace{10px}}) + 5\) \(3=3\)
# 8 \(2(3x - 7) = 3(x + 2) + 4\) Multi-Step Mastery
Show algebraic steps:
\(x =\)
Mosaic Color:
✓ Substitution Check: LHS \(\stackrel{?}{=}\) RHS
\(2(3(\underline{\hspace{8px}})-7) \stackrel{?}{=} 3((\underline{\hspace{8px}})+2)+4\) \(34=34\)
Part 3: Self-Checking Cipher Decoder & Mystery Mosaic
Correct answers unlock an 8-fold symmetrical geometric crest!
Solution Cipher Key: Includes Decoy Traps
\(x = 6\) Cobalt Blue
\(x = -4\) Tangerine
\(x = 3\) Goldenrod
\(x = 7\) Teal Green
\(x = 5\) Crimson Coral
\(x = 4\) Amethyst
\(x = -2\) Sky Azure
\(x = 8\) Emerald Green
\(x = -6\) Lavender
\(x = 2\) Rose Pink
\(x = -3\) Olive Gold
\(x = 12\) Charcoal
Self-Check Protocol: If your calculated solution does not match a valid color above or breaks the medallion's 8-fold radial symmetry, re-evaluate your inverse operations!
1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8
Color all regions matching each problem # to reveal the symmetry
Self-Checking Equation Enigma • Two-Step & Multi-Step Equations Page 2 of 2
