Linear Equations

Linear equation

An equation whose variable appears only to the first power; it has one solution, none, or infinitely many.

$$ax + b = 0 \Rightarrow x = -\frac{b}{a}$$

• Distribute and combine like terms on each side before moving anything.
• Move variable terms to the side where the coefficient stays positive to reduce sign errors.
• Clear fractions by multiplying every term by the least common denominator.
• Identity (infinitely many solutions) and contradiction (no solution) are valid outcomes.

• Distributing to only the first term inside parentheses: $3(x - 2) \ne 3x - 2$.
• Multiplying only some terms when clearing fractions.
• Calling $0 = 0$ the solution $x = 0$.

Try each one, then open the answer. Numerical answers on this page are verified by an automated calculation check.

1. 1.Solve $5x + 3 = 2x - 9$.

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   $x = -4$

2. 2.Solve $\frac{x}{2} + \frac{x}{3} = 10$.

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   $x = 12$

3. 3.Solve $4(x + 1) = 2(x + 8)$.

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   $x = 6$

• Slope and Lines
• Systems of Equations
• Polynomials and Factoring
• All Algebra 1 topics