Linear Equation Breakdown Guide
Algebra I • Mastery Focus Multi-Step Equations
Linear Equation Breakdown
Strategy Reference
Step-by-Step Method
\( ! \)
Mastery Target Problem
Solve for the variable \( x \) and verify the solution.
\( 4(2x - 3) - 3(x + 5) = 2(x - 7) + 5 \)
1
Distribute to Clear Parentheses
Multiply factors across terms inside parentheses. Watch negative signs carefully!
\( 8x - 12 - 3x - 15 = 2x - 14 + 5 \)
2
Combine Like Terms
Combine variable terms and constant terms independently on each side.
\( (8x - 3x) + (-12 - 15) = 2x + (-14 + 5) \)
\( 5x - 27 = 2x - 9 \)
3
Collect Variables on One Side
Subtract \( 2x \) from both sides using the Subtraction Property of Equality.
\( 5x - 2x - 27 = 2x - 2x - 9 \)
\( 3x - 27 = -9 \)
4
Isolate the Variable
Add \( 27 \) to both sides, then divide both sides by \( 3 \).
\( 3x = -9 + 27 \implies 3x = 18 \)
\( x = 6 \)
Step 5 • Verification Check
Substitute \( x = 6 \) back into the original equation:
LHS: \( 4(2(6) - 3) - 3(6 + 5) \)
\( = 4(9) - 3(11) = 36 - 33 = \mathbf{3} \)
RHS: \( 2(6 - 7) + 5 = 2(-1) + 5 = \mathbf{3} \)
\( 3 = 3 \) ✓ Solution Confirmed
Key Watch-Outs
- • Distributing Negatives: Remember \( -3(x + 5) \) becomes \( -3x - 15 \), not \( -3x + 15 \).
- • Signs During Transfer: When moving terms across the equals sign, perform the inverse operation on both sides.
Golden Rule: Keep the equals sign aligned down your page for clean algebra tracking.
Parallel Practice Problem: \( 5(3x - 2) - 2(4x + 1) = 3(2x - 6) + 2 \)
Target Solution: \( x = -4 \)