Solving equations by adding and subtracting involves using opposite operations to isolate a variable. Whatever you add or subtract on one side of an equation, you must also do on the other side to keep the equation balanced. These one-step equations are an important foundation for learning algebra and solving more complicated equations.
Practice Problems
\(\textbf{1)}\) \(x+3=4\)
The answer is \(x=1\)
\(x+3=4\)
\(x+3-3=4-3\) (Subtract 3 from both sides.)
\(x=1\)
The answer is \(x=1\)
\(x+3=4\)
\(x+3-3=4-3\) (Subtract 3 from both sides.)
\(x=1\)
\(\textbf{2)}\) \(x-4=12\)
The answer is \(x=16\)
\(x-4=12\)
\(x-4+4=12+4\) (Add 4 to both sides.)
\(x=16\)
The answer is \(x=16\)
\(x-4=12\)
\(x-4+4=12+4\) (Add 4 to both sides.)
\(x=16\)
\(\textbf{3)}\) \(x+2=-12\)
The answer is \(x=-14\)
\(x+2=-12\)
\(x+2-2=-12-2\) (Subtract 2 from both sides.)
\(x=-14\)
The answer is \(x=-14\)
\(x+2=-12\)
\(x+2-2=-12-2\) (Subtract 2 from both sides.)
\(x=-14\)
\(\textbf{4)}\) \(x-5=-3\)
The answer is \(x=2\)
\(x-5=-3\)
\(x-5+5=-3+5\) (Add 5 to both sides.)
\(x=2\)
The answer is \(x=2\)
\(x-5=-3\)
\(x-5+5=-3+5\) (Add 5 to both sides.)
\(x=2\)
\(\textbf{5)}\) \(4=x-7\)
The answer is \(x=11\)
\(4=x-7\)
\(4+7=x-7+7\) (Add 7 to both sides.)
\(11=x\)
\(x=11\)
The answer is \(x=11\)
\(4=x-7\)
\(4+7=x-7+7\) (Add 7 to both sides.)
\(11=x\)
\(x=11\)
\(\textbf{6)}\) \(-12=x+8\)
The answer is \(x=-20\)
\(-12=x+8\)
\(-12-8=x+8-8\) (Subtract 8 from both sides.)
\(-20=x\)
\(x=-20\)
The answer is \(x=-20\)
\(-12=x+8\)
\(-12-8=x+8-8\) (Subtract 8 from both sides.)
\(-20=x\)
\(x=-20\)
\(\textbf{7)}\) \(x+7=5\)
The answer is \(x=-2\)
\(x+7=5\)
\(x+7-7=5-7\) (Subtract 7 from both sides.)
\(x=-2\)
The answer is \(x=-2\)
\(x+7=5\)
\(x+7-7=5-7\) (Subtract 7 from both sides.)
\(x=-2\)
\(\textbf{8)}\) \(x-5=10\)
The answer is \(x=15\)
\(x-5=10\)
\(x-5+5=10+5\) (Add 5 to both sides.)
\(x=15\)
The answer is \(x=15\)
\(x-5=10\)
\(x-5+5=10+5\) (Add 5 to both sides.)
\(x=15\)
\(\textbf{9)}\) \(x+8=-4\)
The answer is \(x=-12\)
\(x+8=-4\)
\(x+8-8=-4-8\) (Subtract 8 from both sides.)
\(x=-12\)
The answer is \(x=-12\)
\(x+8=-4\)
\(x+8-8=-4-8\) (Subtract 8 from both sides.)
\(x=-12\)
\(\textbf{10)}\) \(x-6=-8\)
The answer is \(x=-2\)
\(x-6=-8\)
\(x-6+6=-8+6\) (Add 6 to both sides.)
\(x=-2\)
The answer is \(x=-2\)
\(x-6=-8\)
\(x-6+6=-8+6\) (Add 6 to both sides.)
\(x=-2\)
\(\textbf{11)}\) \(5=x-3\)
The answer is \(x=8\)
\(5=x-3\)
\(5+3=x-3+3\) (Add 3 to both sides.)
\(8=x\)
\(x=8\)
The answer is \(x=8\)
\(5=x-3\)
\(5+3=x-3+3\) (Add 3 to both sides.)
\(8=x\)
\(x=8\)
\(\textbf{12)}\) \(-4=x+5\)
The answer is \(x=-9\)
\(-4=x+5\)
\(-4-5=x+5-5\) (Subtract 5 from both sides.)
\(-9=x\)
\(x=-9\)
The answer is \(x=-9\)
\(-4=x+5\)
\(-4-5=x+5-5\) (Subtract 5 from both sides.)
\(-9=x\)
\(x=-9\)
\(\textbf{13)}\) \(x+5=9\)
The answer is \(x=4\)
\(x+5=9\)
\(x+5-5=9-5\) (Subtract 5 from both sides.)
\(x=4\)
The answer is \(x=4\)
\(x+5=9\)
\(x+5-5=9-5\) (Subtract 5 from both sides.)
\(x=4\)
\(\textbf{14)}\) \(x-8=10\)
The answer is \(x=18\)
\(x-8=10\)
\(x-8+8=10+8\) (Add 8 to both sides.)
\(x=18\)
The answer is \(x=18\)
\(x-8=10\)
\(x-8+8=10+8\) (Add 8 to both sides.)
\(x=18\)
\(\textbf{15)}\) \(x+4=-18\)
The answer is \(x=-22\)
\(x+4=-18\)
\(x+4-4=-18-4\) (Subtract 4 from both sides.)
\(x=-22\)
The answer is \(x=-22\)
\(x+4=-18\)
\(x+4-4=-18-4\) (Subtract 4 from both sides.)
\(x=-22\)
\(\textbf{16)}\) \(x+11=26\)
The answer is \(x=15\)
\(x+11=26\)
\(x+11-11=26-11\) (Subtract 11 from both sides.)
\(x=15\)
The answer is \(x=15\)
\(x+11=26\)
\(x+11-11=26-11\) (Subtract 11 from both sides.)
\(x=15\)
\(\textbf{17)}\) \(x-13=-20\)
The answer is \(x=-7\)
\(x-13=-20\)
\(x-13+13=-20+13\) (Add 13 to both sides.)
\(x=-7\)
The answer is \(x=-7\)
\(x-13=-20\)
\(x-13+13=-20+13\) (Add 13 to both sides.)
\(x=-7\)
\(\textbf{18)}\) \(x+(-6)=14\)
The answer is \(x=20\)
\(x+(-6)=14\)
\(x-6=14\) (Adding a negative is the same as subtracting.)
\(x-6+6=14+6\) (Add 6 to both sides.)
\(x=20\)
The answer is \(x=20\)
\(x+(-6)=14\)
\(x-6=14\) (Adding a negative is the same as subtracting.)
\(x-6+6=14+6\) (Add 6 to both sides.)
\(x=20\)
\(\textbf{19)}\) \(17=x+(-9)\)
The answer is \(x=26\)
\(17=x+(-9)\)
\(17=x-9\) (Rewrite addition of a negative.)
\(17+9=x-9+9\) (Add 9 to both sides.)
\(26=x\)
\(x=26\)
The answer is \(x=26\)
\(17=x+(-9)\)
\(17=x-9\) (Rewrite addition of a negative.)
\(17+9=x-9+9\) (Add 9 to both sides.)
\(26=x\)
\(x=26\)
\(\textbf{20)}\) \(x-(-7)=12\)
The answer is \(x=5\)
\(x-(-7)=12\)
\(x+7=12\) (Subtracting a negative is the same as adding.)
\(x+7-7=12-7\) (Subtract 7 from both sides.)
\(x=5\)
The answer is \(x=5\)
\(x-(-7)=12\)
\(x+7=12\) (Subtracting a negative is the same as adding.)
\(x+7-7=12-7\) (Subtract 7 from both sides.)
\(x=5\)
\(\textbf{21)}\) \(x+2.5=7.8\)
The answer is \(x=5.3\)
\(x+2.5=7.8\)
\(x+2.5-2.5=7.8-2.5\) (Subtract 2.5 from both sides.)
\(x=5.3\)
The answer is \(x=5.3\)
\(x+2.5=7.8\)
\(x+2.5-2.5=7.8-2.5\) (Subtract 2.5 from both sides.)
\(x=5.3\)
\(\textbf{22)}\) \(x-1.7=-3.2\)
The answer is \(x=-1.5\)
\(x-1.7=-3.2\)
\(x-1.7+1.7=-3.2+1.7\) (Add 1.7 to both sides.)
\(x=-1.5\)
The answer is \(x=-1.5\)
\(x-1.7=-3.2\)
\(x-1.7+1.7=-3.2+1.7\) (Add 1.7 to both sides.)
\(x=-1.5\)
\(\textbf{23)}\) \(x+\frac{1}{4}=\frac{3}{4}\)
The answer is \(x=\frac{1}{2}\)
\(x+\frac{1}{4}=\frac{3}{4}\)
\(x+\frac{1}{4}-\frac{1}{4}=\frac{3}{4}-\frac{1}{4}\) (Subtract 1/4 from both sides.)
\(x=\frac{2}{4}\)
\(x=\frac{1}{2}\) (Simplify the fraction.)
The answer is \(x=\frac{1}{2}\)
\(x+\frac{1}{4}=\frac{3}{4}\)
\(x+\frac{1}{4}-\frac{1}{4}=\frac{3}{4}-\frac{1}{4}\) (Subtract 1/4 from both sides.)
\(x=\frac{2}{4}\)
\(x=\frac{1}{2}\) (Simplify the fraction.)
\(\textbf{24)}\) \(x-\frac{2}{3}=\frac{1}{6}\)
The answer is \(x=\frac{5}{6}\)
\(x-\frac{2}{3}=\frac{1}{6}\)
\(x-\frac{2}{3}+\frac{2}{3}=\frac{1}{6}+\frac{2}{3}\) (Add 2/3 to both sides.)
\(x=\frac{1}{6}+\frac{4}{6}\) (Find a common denominator.)
\(x=\frac{5}{6}\)
The answer is \(x=\frac{5}{6}\)
\(x-\frac{2}{3}=\frac{1}{6}\)
\(x-\frac{2}{3}+\frac{2}{3}=\frac{1}{6}+\frac{2}{3}\) (Add 2/3 to both sides.)
\(x=\frac{1}{6}+\frac{4}{6}\) (Find a common denominator.)
\(x=\frac{5}{6}\)
\(\textbf{25)}\) \(-4.5=x-2.8\)
The answer is \(x=-1.7\)
\(-4.5=x-2.8\)
\(-4.5+2.8=x-2.8+2.8\) (Add 2.8 to both sides.)
\(-1.7=x\)
\(x=-1.7\)
The answer is \(x=-1.7\)
\(-4.5=x-2.8\)
\(-4.5+2.8=x-2.8+2.8\) (Add 2.8 to both sides.)
\(-1.7=x\)
\(x=-1.7\)
See Related Pages
\(\bullet\text{ Equation Calculator (Symbolab.com)}\)
\(\,\,\,\,\,\,\,\,\)
\(\bullet\text{ Solving Equations by Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,x+3=4…\)
\(\bullet\text{ Solving Equations by Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,8x=48…\)
\(\bullet\text{ Solving Multi-step Equations}\)
\(\,\,\,\,\,\,\,\,3x+2=14…\)
\(\bullet\text{ Solving Equations with Variables on Both Sides}\)
\(\,\,\,\,\,\,\,\,3x+5=7x-3…\)
\(\bullet\text{ Solving Equations with Decimals}\)
\(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\)
\(\bullet\text{ Solving Equations with Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\)