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Linear Equations
Select the skills to practice, and then click Go!
1. Foundational skills
Identify the inverse operation
\[ x + 5 = 12 \]
Identify the inverse operation needed to isolate the variable.
2. One-step equations
Addition equations
\[ x + 4 = 9 \]
Solve one-step equations where a number is added.
Subtraction equations
\[ x – 3 = 5 \]
Solve one-step equations where a number is subtracted.
Subtraction from a constant
\[ 10 – x = 3 \]
Solve one-step equations subtracted from a constant.
Multiplication equations
\[ 4x = 28 \]
Solve one-step multiplication equations.
Division equations
\[ \frac{x}{4} = 3 \]
Solve one-step division equations.
3. Two-step equations
Standard two-step equations
\[ 2x + 3 = 11 \]
Solve standard two-step equations.
Division then add/sub
\[ \frac{x}{3} + 2 = 5 \]
Solve division followed by addition/subtraction.
Constant minus multiple
\[ 15 – 2x = 7 \]
Solve equations where multiple is subtracted from constant.
Constant minus divided
\[ 14 – \frac{x}{2} = 10 \]
Solve equations where divided unknown is subtracted.
4. Equations with brackets
Single bracket only
\[ 3(x + 2) = 21 \]
Solve equations with a single bracket.
Bracket with extra term
\[ 2(x + 3) + 5 = 17 \]
Bracket with term added or subtracted outside.
Expression divided
\[ \frac{x + 3}{4} = 2 \]
Solve equations with divided expression.
Divided expression + term
\[ \frac{x + 2}{5} + 1 = 3 \]
Divided expression with additional term.
5. Unknowns on both sides
Simple unknowns both sides
\[ 5x = 2x + 9 \]
Unknowns on both sides, simple.
Complex unknowns on both sides
\[ 3x + 4 = x + 12 \]
Unknowns and constants/subtraction on both sides.
Bracket on one side
\[ 2(x + 4) = x + 13 \]
One bracket and unknowns on both sides.
Brackets on both sides
\[ 3(x + 1) = 2(x + 4) \]
Brackets on both sides.
6. Special cases
Coefficient 1 on one side
\[ x + 5 = 2x – 3 \]
Unknown has coefficient 1 on one side.
Answer after one step
\[ 4x = 3x + 7 \]
Collecting terms solves directly.
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