Solving Linear Equations
Select the skills to practice, and then click Go!
One-Step Equations
Multiplication
\[ 3x = 15 \]
Solve equations where the unknown is multiplied by a number.
Division
\[ \frac{x}{4} = 3 \]
Solve equations involving division.
Addition
\[ x + 7 = 12 \]
Simple equations involving addition.
Subtraction
\[ x – 4 = 6 \]
Simple equations involving subtraction.
Unknown Subtracted
\[ 12 – x = 5 \]
Equations where the unknown is being subtracted.
Two-Step Equations
Multiply then Add
\[ 2x + 5 = 13 \]
Two-step equations with multiplication and addition.
Multiply then Subtract
\[ 3x – 4 = 11 \]
Two-step equations with multiplication and subtraction.
Unknown Term Subtracted
\[ 20 – 3x = 5 \]
Equations like 20 – 3x = 5.
Divide then Add
\[ \frac{x}{3} + 2 = 5 \]
Equations involving division followed by addition.
Divide then Subtract
\[ \frac{x}{2} – 3 = 2 \]
Equations involving division followed by subtraction.
Unknown Divided (Negative)
\[ 10 – \frac{x}{2} = 6 \]
Equations where the fraction is subtracted.
Equations with Brackets
Brackets (Addition)
\[ 2(x + 3) = 14 \]
Expand brackets involving addition.
Brackets (Subtraction)
\[ 3(x – 2) = 12 \]
Expand brackets involving subtraction.
Brackets (Unknown Subtracted)
\[ 2(5 – x) = 6 \]
Expand brackets where x is subtracted.
Brackets + Constant
\[ 2(x + 1) + 3 = 13 \]
Equations with brackets and an extra constant term.
Complex Brackets
\[ 2(6 – x) + 1 = 9 \]
Multi-step equations involving expansion.
Fractional Equations
Fraction (Addition)
\[ \frac{x + 4}{2} = 4 \]
Expression in numerator with addition.
Fraction (Subtraction)
\[ \frac{x – 3}{2} = 3 \]
Expression in numerator with subtraction.
Fraction (Unknown Subtracted)
\[ \frac{10 – x}{2} = 3 \]
Expression where x is subtracted in numerator.
Unknown on Both Sides
Simple Both Sides
\[ 5x + 2 = 3x + 10 \]
Positive coefficients on both sides.
Subtraction on One Side
\[ 2x + 5 = 14 – x \]
Unknown is subtracted on one side.
Subtraction on Both
\[ 20 – 2x = 14 – x \]
Unknown is subtracted on both sides.
Brackets Both Sides
\[ 2(x + 3) = 3(x + 1) \]
Brackets on both sides of the equation.
Mixed Structures
\[ 3(x + 2) = 2(5 – x) \]
Addition in one bracket, subtraction in the other.
Negative Brackets
\[ 2(8 – x) = 3(4 – x) \]
Unknown subtracted inside both brackets.
One Side Bracket
\[ 2(x + 4) = 3x + 2 \]
One side expanded, one side with bracket.
Bracket with Negative
\[ 2(7 – x) = x + 5 \]
Expansion where x is negative.
Complex Both Sides
\[ 2(x + 1) + 4 = 3(x – 1) + 5 \]
Challenge equations with brackets and constants.
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