Grades Sixth Grade Expressions & EquationsSolving One-Variable Equations & Inequalities

Solving One-Variable Equations & Inequalities

📐 Expressions & Equations

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Solving One-Variable Equations & Inequalities

Keep the balance — whatever you do to one side, do to the other.

An equation states that two expressions are equal. To solve for a variable, use inverse operations to isolate it — undoing addition with subtraction, multiplication with division, and so on. An inequality uses <, >, ≤, or ≥ and has a range of solutions shown on a number line.

Solving an Equation: 3x + 5 = 20

1Identify what's happening to x: multiplied by 3, then 5 is added

2Undo in reverse order: subtract 5 from both sides → 3x = 15

3Divide both sides by 3 → x = 5

4Check: 3(5) + 5 = 15 + 5 = 20 ✓

3x + 5 = 20 \implies 3x = 15 \implies x = 5

Equations

Exactly one solution (usually)2x + 1 = 7 → x = 3Check by substituting back

Inequalities

Infinitely many solutions2x + 1 > 7 → x > 3Graph on number line with open/closed circle

When multiplying or dividing an inequality by a negative number, flip the inequality sign.

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Remember This!

Always verify your equation solution by substituting back into the original equation. For inequalities, test a value in the solution set and one outside it.

✏️ Try It!

Solve for x: 5x − 8 = 27

Take Quiz 📝 — 25 Questions