\( 2x + 5 = 19 \implies 2x = 14 \implies \mathbf{x = 7} \)
\( \frac{k-3}{2} = 8 \implies k - 3 = 16 \implies \mathbf{k = 19} \)
\( 3y - 8 = 13 \implies 3y = 21 \implies \mathbf{y = 7} \)
\( 7w + 11 = 60 \implies 7w = 49 \implies \mathbf{w = 7} \)
\( \frac{a}{4} + 7 = 12 \implies \frac{a}{4} = 5 \implies \mathbf{a = 20} \)
\( -6b + 18 = -12 \implies -6b = -30 \implies \mathbf{b = 5} \)
\( 5m + 14 = -6 \implies 5m = -20 \implies \mathbf{m = -4} \)
\( \frac{n}{5} - 6 = 2 \implies \frac{n}{5} = 8 \implies \mathbf{n = 40} \)
\( -4p - 9 = 15 \implies -4p = 24 \implies \mathbf{p = -6} \)
\( 10 - 3z = 25 \implies -3z = 15 \implies \mathbf{z = -5} \)
Equation Solvers Teacher Reference • Solutions 1–20 Page 1 of 2 • Turn over for Multi-Step
Level 3 Solutions Algebra I • Detailed Step Progression
Worksheet 3 Key
Problem 1 \( x = 4 \)
\( 3x + 4x - 5 = 23 \)
\( \implies 7x - 5 = 23 \)
\( \implies 7x = 28 \implies \mathbf{x = 4} \)
Problem 2 \( y = 5 \)
\( 2(3y - 4) = 22 \)
\( \implies 6y - 8 = 22 \)
\( \implies 6y = 30 \implies \mathbf{y = 5} \)
Problem 3 \( a = 5 \)
\( 5a - 8 = 2a + 7 \)
\( \implies 3a - 8 = 7 \)
\( \implies 3a = 15 \implies \mathbf{a = 5} \)
Problem 4 \( m = 9 \)
\( 4(m + 2) - 3m = 17 \)
\( \implies 4m + 8 - 3m = 17 \)
\( \implies m + 8 = 17 \implies \mathbf{m = 9} \)
Problem 5 \( p = -5 \)
\( 8p + 6 = 3p - 19 \)
\( \implies 5p + 6 = -19 \)
\( \implies 5p = -25 \implies \mathbf{p = -5} \)
Problem 6 \( k = 6 \)
\( 3(2k - 1) = 4k + 9 \)
\( \implies 6k - 3 = 4k + 9 \)
\( \implies 2k = 12 \implies \mathbf{k = 6} \)
Problem 7 \( w = 7 \)
\( 2(w + 5) = 4(w - 1) \)
\( \implies 2w + 10 = 4w - 4 \)
\( \implies 14 = 2w \implies \mathbf{w = 7} \)
Problem 8 \( n = 4 \)
\( 15 - 2(3n + 1) = -11 \)
\( \implies 15 - 6n - 2 = -11 \)
\( \implies 13 - 6n = -11 \implies \mathbf{n = 4} \)
Problem 9 \( z = 12 \)
\( 5(z - 2) = 2(2z + 1) \)
\( \implies 5z - 10 = 4z + 2 \)
\( \implies z - 10 = 2 \implies \mathbf{z = 12} \)
Problem 10 \( t = -5 \)
\( -2(4t - 3) + 5t = 21 \)
\( \implies -8t + 6 + 5t = 21 \)
\( \implies -3t + 6 = 21 \implies \mathbf{t = -5} \)
Common Student Misconceptions to Watch For:
Distributing Negatives: In #8 and #10, students frequently forget to distribute the negative to the second term (e.g., writing \(-2(+1) = +2\) instead of \(-2\)).
Variables on Both Sides: In #3, #6, and #7, remind students to collect variables on one side before constants to prevent double-canceling.
Like Terms vs Inverses: On #1 and #4, ensure students combine terms on the same side without applying opposite inverse operations.
Equation Solvers Teacher Reference • Solutions 21–30 Page 2 of 2
