Additive property of equality

High School

Definition

The property states that if a = b then a + c = b + c. When solving equations, variables or terms that equal can be substituted in and out with each other. For equations with multiple variables and terms, this property can be used to substitute and collect like terms to solve for one variable.

Worked examples

\(x - 5 = 12 \)→\( x - 5 + 5 = 12 + 5 \)→\( x = 17\)

Add 5 to both sides to keep the equation balanced and isolate x.

\(3a + 7 = 2a + 15 \)→\( 3a + 7 - 2a = 2a + 15 - 2a \)→\( a + 7 = 15\)

Subtract \(2a\) from both sides to collect like terms on one side.

Common mistakes

\(x - 5 = 12 \)→\( x = 12 + 5\) (forgot to add 5 to the right side) → \(x - 5 = 12 \)→\( x - 5 + 5 = 12 + 5 \)→\( x = 17\) You must add the same quantity to both sides to preserve equality.
\(x + 3 = 10 \)→\( x = 10 + 3\) → \(x + 3 = 10 \)→\( x + 3 - 3 = 10 - 3 \)→\( x = 7\) Adding 3 to both sides moves in the wrong direction; subtract 3 to isolate x.
\(2x + 5 = 9 \)→\( 2x = 9 + 5\) → \(2x + 5 = 9 \)→\( 2x + 5 - 5 = 9 - 5 \)→\( 2x = 4\) Subtracting 5 from both sides removes it from the left; don't add it to the right.

Where you'll use it next

You'll use this property constantly when solving linear equations, systems of equations, and later algebraic manipulations in higher math, including solving inequalities and working with formulas in geometry and physics.

Found in 1 StudyPug lesson

Mastering One-Step Equations: x + a = b

Grade 7 Math

Unlock the power of one-step equations! Learn essential properties, solve x + a = b effortlessly, and apply your skills to real-world problems. Boost your algebra confidence today.

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