Algebra — Equations
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Linear Equations & Inequalities

⚖️ Algebra — Equations
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Linear Equations & Inequalities

Solve and graph linear equations and inequalities on a number line and coordinate plane.

A linear equation in one variable has the form ax + b = c, where a ≠ 0. The solution is the value of x that makes the equation true. Linear inequalities are solved the same way, except multiplying or dividing by a negative number reverses the inequality sign.

ax+b=c  ⟹  x=c−baax + b = c \implies x = \frac{c - b}{a}

Solving a Linear Equation

1Distribute and combine like terms on each side.
2Move all variable terms to one side using inverse operations.
3Move all constant terms to the other side.
4Divide both sides by the coefficient of the variable.
5Check your solution in the original equation.
3(2x−4)=x+11  ⟹  6x−12=x+11  ⟹  5x=23  ⟹  x=2353(2x - 4) = x + 11 \implies 6x - 12 = x + 11 \implies 5x = 23 \implies x = \frac{23}{5}
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Key inequality rule: when you multiply or divide both sides by a negative number, flip the inequality sign. For example, −2x > 6 gives x < −3.

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Remember This!

Graph linear inequalities on a number line: use an open circle (○) for strict inequalities (< or >) and a closed circle (●) for ≤ or ≥.

✏️ Try It!

Solve for x: 2(x − 3) + 4 = 3x − 5

Practice with CalcVerse
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