One-Step Equations

Learn additive inverse operations, multiplicative inverse operations.

Lesson 1 of 32 parts Practice Flashcards

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Additive Inverse Operations

Objective: Explain additive inverse operations, apply the stated method, and check its conditions.

An equation describes values making two expressions equal. Adding or subtracting the same number on both sides preserves its solution set. To undo x+b, subtract b from both sides and check the result in the original equation. Apply the inverse operation to both sides.

Formulas

$x+b=d ⇒ x=d−b$

Worked examples

Try itSolve x+7=14.Show answer

Step 1: Subtract 7 from both sides. Step 2: x=14−7. Step 3: x=7; substitution checks the equality.

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Additive Inverse Operations

Objective: Explain additive inverse operations, apply the stated method, and check its conditions.

Formulas

$x+b=d ⇒ x=d−b$

Worked examples

Try itSolve x+7=14.Show answer

Step 1: Subtract 7 from both sides. Step 2: x=14−7. Step 3: x=7; substitution checks the equality.

Multiplicative Inverse Operations

Objective: Explain multiplicative inverse operations, apply the stated method, and check its conditions.

For ax=d with a≠0, divide both sides by a to isolate x. Multiplication or division by a nonzero constant preserves equality. If a=0, dividing is invalid and the original equation must be examined separately. Never divide an equation by zero.

Formulas

$ax=d ⇒ x=d/a, a≠0$

Worked examples

Try itSolve 6x=42.Show answer

Step 1: Divide both sides by nonzero 6. Step 2: x=42/6. Step 3: x=7.

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