Solve for x
Solving equations with fractions involves using inverse operations to isolate the variable. When a fraction is multiplied by a variable, multiplying both sides by the reciprocal can help solve the equation. For multi-step equations, simplify and undo addition or subtraction before multiplying by the reciprocal. Remember that any operation performed on one side of an equation must also be performed on the other side.
Practice Problems
\(\textbf{1)}\) \(\frac{2}{5}x=8\) The answer is \(x=20\) \(\frac{5}{2}\cdot\frac{2}{5}x=8\cdot\frac{5}{2}\)
\(\frac{10}{10}x=\frac{8}{1}\cdot\frac{5}{2}\)
\(x=\frac{40}{2}\)
The answer is \(x=20\)
\(\frac{10}{10}x=\frac{8}{1}\cdot\frac{5}{2}\)
\(x=\frac{40}{2}\)
The answer is \(x=20\)
\(\textbf{2)}\) \(\frac{3}{4}x=6\) The answer is \(x=8\) \(\frac{4}{3}\cdot\frac{3}{4}x=6\cdot\frac{4}{3}\)
\(\frac{12}{12}x=\frac{6}{1}\cdot\frac{4}{3}\)
\(x=\frac{24}{3}\)
The answer is \(x=8\)
\(\frac{12}{12}x=\frac{6}{1}\cdot\frac{4}{3}\)
\(x=\frac{24}{3}\)
The answer is \(x=8\)
\(\textbf{3)}\) \(\frac{7}{8}x=21\) The answer is \(x=24\) \(\frac{8}{7}\cdot\frac{7}{8}x=21\cdot\frac{8}{7}\)
\(x=3\cdot8\)
The answer is \(x=24\)
\(x=3\cdot8\)
The answer is \(x=24\)
\(\textbf{4)}\) \(\frac{3}{5}x+3=15\) The answer is \(x=20\) \(\frac{3}{5}x+3=15\)
\(\frac{3}{5}x=12\)
\(\frac{5}{3}\cdot\frac{3}{5}x=12\cdot\frac{5}{3}\)
\(x=\frac{60}{3}\)
The answer is \(x=20\)
\(\frac{3}{5}x=12\)
\(\frac{5}{3}\cdot\frac{3}{5}x=12\cdot\frac{5}{3}\)
\(x=\frac{60}{3}\)
The answer is \(x=20\)
\(\textbf{5)}\) \(\frac{4}{5}x-7=-3\) The answer is \(x=5\) \(\frac{4}{5}x-7=-3\)
\(\frac{4}{5}x=4\)
\(\frac{5}{4}\cdot\frac{4}{5}x=4\cdot\frac{5}{4}\)
\(x=\frac{20}{4}\)
The answer is \(x=5\)
\(\frac{4}{5}x=4\)
\(\frac{5}{4}\cdot\frac{4}{5}x=4\cdot\frac{5}{4}\)
\(x=\frac{20}{4}\)
The answer is \(x=5\)
\(\textbf{6)}\) \(\frac{5}{6}x=15\) The answer is \(x=18\) \(\frac{5}{6}x=15\)
\(\frac{6}{5}\cdot\frac{5}{6}x=15\cdot\frac{6}{5}\)
\(x=\frac{90}{5}\)
The answer is \(x=18\)
\(\frac{6}{5}\cdot\frac{5}{6}x=15\cdot\frac{6}{5}\)
\(x=\frac{90}{5}\)
The answer is \(x=18\)
\(\textbf{7)}\) \(\frac{2}{3}x=-10\) The answer is \(x=-15\) \(\frac{2}{3}x=-10\)
\(\frac{3}{2}\cdot\frac{2}{3}x=-10\cdot\frac{3}{2}\)
\(x=\frac{-30}{2}\)
The answer is \(x=-15\)
\(\frac{3}{2}\cdot\frac{2}{3}x=-10\cdot\frac{3}{2}\)
\(x=\frac{-30}{2}\)
The answer is \(x=-15\)
\(\textbf{8)}\) \(-\frac{3}{7}x=12\) The answer is \(x=-28\) \(-\frac{3}{7}x=12\)
\(-\frac{7}{3}\cdot\left(-\frac{3}{7}\right)x=12\cdot\left(-\frac{7}{3}\right)\)
\(x=\frac{-84}{3}\)
The answer is \(x=-28\)
\(-\frac{7}{3}\cdot\left(-\frac{3}{7}\right)x=12\cdot\left(-\frac{7}{3}\right)\)
\(x=\frac{-84}{3}\)
The answer is \(x=-28\)
\(\textbf{9)}\) \(\frac{5}{8}x+4=19\) The answer is \(x=24\) \(\frac{5}{8}x+4=19\)
\(\frac{5}{8}x=15\)
\(\frac{8}{5}\cdot\frac{5}{8}x=15\cdot\frac{8}{5}\)
\(x=\frac{120}{5}\)
The answer is \(x=24\)
\(\frac{5}{8}x=15\)
\(\frac{8}{5}\cdot\frac{5}{8}x=15\cdot\frac{8}{5}\)
\(x=\frac{120}{5}\)
The answer is \(x=24\)
\(\textbf{10)}\) \(\frac{3}{4}x-5=7\) The answer is \(x=16\) \(\frac{3}{4}x-5=7\)
\(\frac{3}{4}x=12\)
\(\frac{4}{3}\cdot\frac{3}{4}x=12\cdot\frac{4}{3}\)
\(x=\frac{48}{3}\)
The answer is \(x=16\)
\(\frac{3}{4}x=12\)
\(\frac{4}{3}\cdot\frac{3}{4}x=12\cdot\frac{4}{3}\)
\(x=\frac{48}{3}\)
The answer is \(x=16\)
\(\textbf{11)}\) \(\frac{2}{5}x+7=3\) The answer is \(x=-10\) \(\frac{2}{5}x+7=3\)
\(\frac{2}{5}x=-4\)
\(\frac{5}{2}\cdot\frac{2}{5}x=-4\cdot\frac{5}{2}\)
\(x=\frac{-20}{2}\)
The answer is \(x=-10\)
\(\frac{2}{5}x=-4\)
\(\frac{5}{2}\cdot\frac{2}{5}x=-4\cdot\frac{5}{2}\)
\(x=\frac{-20}{2}\)
The answer is \(x=-10\)
\(\textbf{12)}\) \(-\frac{3}{4}x+2=11\) The answer is \(x=-12\) \(-\frac{3}{4}x+2=11\)
\(-\frac{3}{4}x=9\)
\(-\frac{4}{3}\cdot\left(-\frac{3}{4}\right)x=9\cdot\left(-\frac{4}{3}\right)\)
\(x=\frac{-36}{3}\)
The answer is \(x=-12\)
\(-\frac{3}{4}x=9\)
\(-\frac{4}{3}\cdot\left(-\frac{3}{4}\right)x=9\cdot\left(-\frac{4}{3}\right)\)
\(x=\frac{-36}{3}\)
The answer is \(x=-12\)
\(\textbf{13)}\) \(\frac{x}{6}+5=9\) The answer is \(x=24\) \(\frac{x}{6}+5=9\)
\(\frac{x}{6}=4\)
\(6\cdot\frac{x}{6}=4\cdot6\)
The answer is \(x=24\)
\(\frac{x}{6}=4\)
\(6\cdot\frac{x}{6}=4\cdot6\)
The answer is \(x=24\)
\(\textbf{14)}\) \(\frac{x-3}{4}=5\) The answer is \(x=23\) \(\frac{x-3}{4}=5\)
\(4\cdot\frac{x-3}{4}=5\cdot4\)
\(x-3=20\)
\(x=20+3\)
The answer is \(x=23\)
\(4\cdot\frac{x-3}{4}=5\cdot4\)
\(x-3=20\)
\(x=20+3\)
The answer is \(x=23\)
\(\textbf{15)}\) \(\frac{2x+1}{3}=7\) The answer is \(x=10\) \(\frac{2x+1}{3}=7\)
\(2x+1=21\)
\(2x=20\)
\(x=\frac{20}{2}\)
The answer is \(x=10\)
\(2x+1=21\)
\(2x=20\)
\(x=\frac{20}{2}\)
The answer is \(x=10\)
\(\textbf{16)}\) \(\frac{1}{2}x+\frac{1}{3}x=10\) The answer is \(x=12\) \(\frac{1}{2}x+\frac{1}{3}x=10\)
\(\frac{3}{6}x+\frac{2}{6}x=10\)
\(\frac{5}{6}x=10\)
\(x=10\cdot\frac{6}{5}\)
The answer is \(x=12\)
\(\frac{3}{6}x+\frac{2}{6}x=10\)
\(\frac{5}{6}x=10\)
\(x=10\cdot\frac{6}{5}\)
The answer is \(x=12\)
\(\textbf{17)}\) \(\frac{3}{4}x-\frac{1}{2}x=6\) The answer is \(x=24\) \(\frac{3}{4}x-\frac{1}{2}x=6\)
\(\frac{3}{4}x-\frac{2}{4}x=6\)
\(\frac{1}{4}x=6\)
\(x=6\cdot4\)
The answer is \(x=24\)
\(\frac{3}{4}x-\frac{2}{4}x=6\)
\(\frac{1}{4}x=6\)
\(x=6\cdot4\)
The answer is \(x=24\)
\(\textbf{18)}\) \(\frac{2}{3}(x+6)=10\) The answer is \(x=9\) \(\frac{2}{3}(x+6)=10\)
\(x+6=10\cdot\frac{3}{2}\)
\(x+6=15\)
\(x=15-6\)
The answer is \(x=9\)
\(x+6=10\cdot\frac{3}{2}\)
\(x+6=15\)
\(x=15-6\)
The answer is \(x=9\)
\(\textbf{19)}\) \(\frac{x}{4}+\frac{x}{6}=5\) The answer is \(x=12\) \(\frac{x}{4}+\frac{x}{6}=5\)
\(\frac{3x}{12}+\frac{2x}{12}=5\)
\(\frac{5x}{12}=5\)
\(x=5\cdot\frac{12}{5}\)
The answer is \(x=12\)
\(\frac{3x}{12}+\frac{2x}{12}=5\)
\(\frac{5x}{12}=5\)
\(x=5\cdot\frac{12}{5}\)
The answer is \(x=12\)
\(\textbf{20)}\) \(\frac{3}{5}x+4=\frac{1}{5}x+12\) The answer is \(x=20\) \(\frac{3}{5}x+4=\frac{1}{5}x+12\)
\(\frac{2}{5}x+4=12\)
\(\frac{2}{5}x=8\)
\(x=8\cdot\frac{5}{2}\)
The answer is \(x=20\)
\(\frac{2}{5}x+4=12\)
\(\frac{2}{5}x=8\)
\(x=8\cdot\frac{5}{2}\)
The answer is \(x=20\)
See Related Pages
\(\bullet\text{ Equation Calculator }\)
\(\,\,\,\,\,\,\,\,\text{(Symbolab.com)}\)
\(\bullet\text{ Solving Equations by Addition and Subtraction}\)
\(\,\,\,\,\,\,\,\,x+3=4…\)
\(\bullet\text{ Solving Equations by Multiplication and Division}\)
\(\,\,\,\,\,\,\,\,8x=48…\)
\(\bullet\text{ Solving Multi-step Equations}\)
\(\,\,\,\,\,\,\,\,3x+2=14…\)
\(\bullet\text{ Solving Equations with Variables on Both Sides}\)
\(\,\,\,\,\,\,\,\,3x+5=7x-3…\)
\(\bullet\text{ Solving Equations with Decimals}\)
\(\,\,\,\,\,\,\,\,43.5+0.2x=51.1…\)
\(\bullet\text{ Solving Equations with Fractions}\)
\(\,\,\,\,\,\,\,\,\frac{2}{5}x+\frac{2}{3}=\frac{8}{3}…\)