Equation Blitz Slides
DO NOW • 5-MINUTE WARM-UP Algebra Readiness
Target: 5:00
Mixed Challenge Edition
Two-Step Equation
Power Blitz
Four equations. Four distinct hurdles: whole numbers, negatives, decimals, and fractions. Solve each problem independently in your notebook.
1
Open Notebooks
Number problems 1 through 4
2
Show Both Steps
Write out both inverse operations
3
Box Final Value
Check solution by substitution
Independent Challenge
Solve for the Variable
Show all work in your notebook
Problem 1 Integers & Negatives
\( -5x + 18 = -37 \)
Solve for x 2 Steps
Problem 2 Decimals
\( 1.4y - 6.2 = 7.8 \)
Solve for y 2 Steps
Problem 3 Fraction Coefficient
\( \frac{3}{5}w + 9 = -6 \)
Solve for w 2 Steps
Problem 4 Division & Negatives
\( \frac{m}{-4} - 3.5 = 2.5 \)
Solve for m Boss Level
Goal: Completely isolate each variable and box your final numerical solution.
Self-check follows in 5 min
Step-By-Step Solution Key
Review: Problems 1 & 2
Self-Check Phase 1
Problem 1: Integers \( -5x + 18 = -37 \)
Step 1: Undo Addition
Subtract \(18\) from both sides
\( -5x = -55 \)
Step 2: Undo Multiplication
Divide both sides by \(-5\)
\( x = \frac{-55}{-5} \)
Final Solution:
\( x = 11 \)
Problem 2: Decimals \( 1.4y - 6.2 = 7.8 \)
Step 1: Undo Subtraction
Add \(6.2\) to both sides
\( 1.4y = 14.0 \)
Step 2: Undo Multiplication
Divide both sides by \(1.4\)
\( y = \frac{14}{1.4} \)
Final Solution:
\( y = 10 \)
Verification: \( -5(11) + 18 = -55 + 18 = -37 \) ✓ \( 1.4(10) - 6.2 = 14 - 6.2 = 7.8 \) ✓
Step-By-Step Solution Key
Review: Problems 3 & 4
Self-Check Phase 2
Problem 3: Fraction \( \frac{3}{5}w + 9 = -6 \)
Step 1: Undo Constant
Subtract \(9\) from both sides
\( \frac{3}{5}w = -15 \)
Step 2: Multiply by Reciprocal
Multiply both sides by \( \frac{5}{3} \)
\( w = -15 \cdot \frac{5}{3} \)
Final Solution:
\( w = -25 \)
Problem 4: Division / Neg \( \frac{m}{-4} - 3.5 = 2.5 \)
Step 1: Undo Subtraction
Add \(3.5\) to both sides
\( \frac{m}{-4} = 6.0 \)
Step 2: Undo Division
Multiply both sides by \(-4\)
\( m = 6 \cdot (-4) \)
Final Solution:
\( m = -24 \)
Verification: \( \frac{3}{5}(-25) + 9 = -15 + 9 = -6 \) ✓ \( \frac{-24}{-4} - 3.5 = 6 - 3.5 = 2.5 \) ✓
Debrief & Reflection
Common Pitfalls & Self-Rating
Mastery Check
Negative Coefficients
In Problem 1, did you divide by -5 or accidentally drop the negative sign?
A negative divided by a negative yields a positive.
Reciprocal Flip
In Problem 3, dividing by \(\frac{3}{5}\) is multiplying by \(\frac{5}{3}\), not \(\frac{3}{5}\).
\(-15 \div 3 = -5\), then \(-5 \times 5 = -25\).
Inverse of Negatives
In Problem 4, to cancel -3.5, did you add \(3.5\) to get \(6.0\)?
\(2.5 + 3.5 = 6.0\), then \(6.0 \times (-4) = -24\).
Score Your Warm-Up:
4/4 Master 3/4 Strong 1-2/4 Keep Practicing
Ready for today's lesson!
