Equation Balance Lab Worksheet
Equation Balance Lab
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Date:
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#1 \(2(3x + 1) + 4x = 7x + 14 - x\)
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Solution: \(x = \) ________
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LHS = RHS
#2 \(3(2y - 1) + 5y = 5y + 13 - 2y\)
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Solution: \(y = \) ________
Check
LHS = RHS
#3 \(4(2m - 3) - 3m = 3m + 4 - 2m\)
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Solution: \(m = \) ________
Check
LHS = RHS
#4 \(5(a + 2) + 2a = 6a + 25 - 2a\)
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Solution: \(a = \) ________
Check
LHS = RHS
#5 \(6(w - 1) - 2w = 3w + 12 - 2w\)
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Solution: \(w = \) ________
Check
LHS = RHS
#6 \(3(3x + 1) - 4x = 4x + 15 - 2x\)
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Solution: \(x = \) ________
Check
LHS = RHS
Equation Balance Lab Page 1 of 2
Equation Balance Lab
Name:
Date:
Period:
#7 \(-2(4k - 3) + 5k = 2(k + 4) - 4k\)
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Solution: \(k = \) ________
Check
LHS = RHS
#8 \(5(2n - 1) - 4n = 2(n + 5) + n\)
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Solution: \(n = \) ________
Check
LHS = RHS
#9 \(3(3p - 2) - 4p = 2(p + 1) + p\)
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Solution: \(p = \) ________
Check
LHS = RHS
#10 \(4(2x - 1) - 3x = 2(x + 1) + x\)
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Solution: \(x = \) ________
Check
LHS = RHS
#11 \(-2(3y - 2) + 4y = 2(2y + 5) - 5y\)
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Solution: \(y = \) ________
Check
LHS = RHS
#12 \(6(2m - 1) - 7m = 2(m + 1) + m\)
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Solution: \(m = \) ________
Check
LHS = RHS
Equation Balance Lab Page 2 of 2
Equation Balance Lab Answer Key
Answer Key
Equation Balance Lab • Solutions (1–6)
Page 1 of 2
#1 \(2(3x + 1) + 4x = 7x + 14 - x\) \(x = 3\)
Step-by-Step Solution
Dist: \(6x + 2 + 4x = 7x + 14 - x\)
Comb: \(10x + 2 = 6x + 14\)
\(-6x\): \(4x + 2 = 14\)
\(-2\): \(4x = 12\)
\(\div 4\): \(x = 3\)
Solution: \(x = 3\)
Substitution Check
\(2(3(\mathbf{3}) + 1) + 4(\mathbf{3})\)
\(\stackrel{?}{=} 7(\mathbf{3}) + 14 - \mathbf{3}\)
\(2(10) + 12 \stackrel{?}{=} 21 + 14 - 3\)
\(32 = 32\) ✓
Verified Balanced
#2 \(3(2y - 1) + 5y = 5y + 13 - 2y\) \(y = 2\)
Step-by-Step Solution
Dist: \(6y - 3 + 5y = 5y + 13 - 2y\)
Comb: \(11y - 3 = 3y + 13\)
\(-3y\): \(8y - 3 = 13\)
\(+3\): \(8y = 16\)
\(\div 8\): \(y = 2\)
Solution: \(y = 2\)
Substitution Check
\(3(2(\mathbf{2}) - 1) + 5(\mathbf{2})\)
\(\stackrel{?}{=} 5(\mathbf{2}) + 13 - 2(\mathbf{2})\)
\(3(3) + 10 \stackrel{?}{=} 10 + 13 - 4\)
\(19 = 19\) ✓
Verified Balanced
#3 \(4(2m - 3) - 3m = 3m + 4 - 2m\) \(m = 4\)
Step-by-Step Solution
Dist: \(8m - 12 - 3m = 3m + 4 - 2m\)
Comb: \(5m - 12 = m + 4\)
\(-m\): \(4m - 12 = 4\)
\(+12\): \(4m = 16\)
\(\div 4\): \(m = 4\)
Solution: \(m = 4\)
Substitution Check
\(4(2(\mathbf{4}) - 3) - 3(\mathbf{4})\)
\(\stackrel{?}{=} 3(\mathbf{4}) + 4 - 2(\mathbf{4})\)
\(4(5) - 12 \stackrel{?}{=} 12 + 4 - 8\)
\(8 = 8\) ✓
Verified Balanced
#4 \(5(a + 2) + 2a = 6a + 25 - 2a\) \(a = 5\)
Step-by-Step Solution
Dist: \(5a + 10 + 2a = 6a + 25 - 2a\)
Comb: \(7a + 10 = 4a + 25\)
\(-4a\): \(3a + 10 = 25\)
\(-10\): \(3a = 15\)
\(\div 3\): \(a = 5\)
Solution: \(a = 5\)
Substitution Check
\(5(\mathbf{5} + 2) + 2(\mathbf{5})\)
\(\stackrel{?}{=} 6(\mathbf{5}) + 25 - 2(\mathbf{5})\)
\(5(7) + 10 \stackrel{?}{=} 30 + 25 - 10\)
\(45 = 45\) ✓
Verified Balanced
#5 \(6(w - 1) - 2w = 3w + 12 - 2w\) \(w = 6\)
Step-by-Step Solution
Dist: \(6w - 6 - 2w = 3w + 12 - 2w\)
Comb: \(4w - 6 = w + 12\)
\(-w\): \(3w - 6 = 12\)
\(+6\): \(3w = 18\)
\(\div 3\): \(w = 6\)
Solution: \(w = 6\)
Substitution Check
\(6(\mathbf{6} - 1) - 2(\mathbf{6})\)
\(\stackrel{?}{=} 3(\mathbf{6}) + 12 - 2(\mathbf{6})\)
\(6(5) - 12 \stackrel{?}{=} 18 + 12 - 12\)
\(18 = 18\) ✓
Verified Balanced
#6 \(3(3x + 1) - 4x = 4x + 15 - 2x\) \(x = 4\)
Step-by-Step Solution
Dist: \(9x + 3 - 4x = 4x + 15 - 2x\)
Comb: \(5x + 3 = 2x + 15\)
\(-2x\): \(3x + 3 = 15\)
\(-3\): \(3x = 12\)
\(\div 3\): \(x = 4\)
Solution: \(x = 4\)
Substitution Check
\(3(3(\mathbf{4}) + 1) - 4(\mathbf{4})\)
\(\stackrel{?}{=} 4(\mathbf{4}) + 15 - 2(\mathbf{4})\)
\(3(13) - 16 \stackrel{?}{=} 16 + 15 - 8\)
\(23 = 23\) ✓
Verified Balanced
Equation Balance Lab • Teacher Reference Page 1 of 2
Answer Key
Equation Balance Lab • Solutions (7–12)
Page 2 of 2
#7 \(-2(4k - 3) + 5k = 2(k + 4) - 4k\) \(k = -2\)
Step-by-Step Solution
Dist: \(-8k + 6 + 5k = 2k + 8 - 4k\)
Comb: \(-3k + 6 = -2k + 8\)
\(+2k\): \(-k + 6 = 8\)
\(-6\): \(-k = 2\)
\(\times -1\): \(k = -2\)
Solution: \(k = -2\)
Substitution Check
\(-2(4(\mathbf{-2}) - 3) + 5(\mathbf{-2})\)
\(\stackrel{?}{=} 2(\mathbf{-2} + 4) - 4(\mathbf{-2})\)
\(-2(-11) - 10 \stackrel{?}{=} 2(2) + 8\)
\(12 = 12\) ✓
Verified Balanced
#8 \(5(2n - 1) - 4n = 2(n + 5) + n\) \(n = 5\)
Step-by-Step Solution
Dist: \(10n - 5 - 4n = 2n + 10 + n\)
Comb: \(6n - 5 = 3n + 10\)
\(-3n\): \(3n - 5 = 10\)
\(+5\): \(3n = 15\)
\(\div 3\): \(n = 5\)
Solution: \(n = 5\)
Substitution Check
\(5(2(\mathbf{5}) - 1) - 4(\mathbf{5})\)
\(\stackrel{?}{=} 2(\mathbf{5} + 5) + \mathbf{5}\)
\(5(9) - 20 \stackrel{?}{=} 2(10) + 5\)
\(25 = 25\) ✓
Verified Balanced
#9 \(3(3p - 2) - 4p = 2(p + 1) + p\) \(p = 4\)
Step-by-Step Solution
Dist: \(9p - 6 - 4p = 2p + 2 + p\)
Comb: \(5p - 6 = 3p + 2\)
\(-3p\): \(2p - 6 = 2\)
\(+6\): \(2p = 8\)
\(\div 2\): \(p = 4\)
Solution: \(p = 4\)
Substitution Check
\(3(3(\mathbf{4}) - 2) - 4(\mathbf{4})\)
\(\stackrel{?}{=} 2(\mathbf{4} + 1) + \mathbf{4}\)
\(3(10) - 16 \stackrel{?}{=} 2(5) + 4\)
\(14 = 14\) ✓
Verified Balanced
#10 \(4(2x - 1) - 3x = 2(x + 1) + x\) \(x = 3\)
Step-by-Step Solution
Dist: \(8x - 4 - 3x = 2x + 2 + x\)
Comb: \(5x - 4 = 3x + 2\)
\(-3x\): \(2x - 4 = 2\)
\(+4\): \(2x = 6\)
\(\div 2\): \(x = 3\)
Solution: \(x = 3\)
Substitution Check
\(4(2(\mathbf{3}) - 1) - 3(\mathbf{3})\)
\(\stackrel{?}{=} 2(\mathbf{3} + 1) + \mathbf{3}\)
\(4(5) - 9 \stackrel{?}{=} 2(4) + 3\)
\(11 = 11\) ✓
Verified Balanced
#11 \(-2(3y - 2) + 4y = 2(2y + 5) - 5y\) \(y = -6\)
Step-by-Step Solution
Dist: \(-6y + 4 + 4y = 4y + 10 - 5y\)
Comb: \(-2y + 4 = -y + 10\)
\(+y\): \(-y + 4 = 10\)
\(-4\): \(-y = 6\)
\(\times -1\): \(y = -6\)
Solution: \(y = -6\)
Substitution Check
\(-2(3(\mathbf{-6}) - 2) + 4(\mathbf{-6})\)
\(\stackrel{?}{=} 2(2(\mathbf{-6}) + 5) - 5(\mathbf{-6})\)
\(-2(-20) - 24 \stackrel{?}{=} 2(-7) + 30\)
\(16 = 16\) ✓
Verified Balanced
#12 \(6(2m - 1) - 7m = 2(m + 1) + m\) \(m = 4\)
Step-by-Step Solution
Dist: \(12m - 6 - 7m = 2m + 2 + m\)
Comb: \(5m - 6 = 3m + 2\)
\(-3m\): \(2m - 6 = 2\)
\(+6\): \(2m = 8\)
\(\div 2\): \(m = 4\)
Solution: \(m = 4\)
Substitution Check
\(6(2(\mathbf{4}) - 1) - 7(\mathbf{4})\)
\(\stackrel{?}{=} 2(\mathbf{4} + 1) + \mathbf{4}\)
\(6(7) - 28 \stackrel{?}{=} 2(5) + 4\)
\(14 = 14\) ✓
Verified Balanced
Equation Balance Lab • Teacher Reference Page 2 of 2
