4-2 Apply Properties of Equality

If two expressions are equal, dividing both sides by the same non-zero number keeps the equality true. For example, if $$7n = 28$$ , then $$7n \div 7 = 28 \div 7$$ .

If two expressions are equal, adding the same number to both sides keeps the equality true. For example, if $$x = 5$$ , then $$x + 3 = 5 + 3$$ .

If two expressions are equal, subtracting the same number from both sides keeps the equality true. For example, if $$y = 10$$ , then $$y - 2 = 10 - 2$$ .

If two expressions are equal, multiplying both sides by the same non-zero number keeps the equality true. For example, if $$a = 4$$ , then $$a \times 2 = 4 \times 2$$ .

An equivalent equation is an equation that has the same solution as another equation. For example, $$n + 4 = 11$$ is equivalent to $$n = 7$$ .

Subtract 4 from both sides: $$n + 4 - 4 = 11 - 4$$ , which simplifies to $$n = 7$$ .

Applying the properties of equality means using these properties to manipulate equations to find unknown values.

Dividing both sides by 4 gives $$m = 15$$ .

You can add the same number to both sides, for example, $$4m + 2 = 60 + 2$$ , which simplifies to $$4m + 2 = 62$$ .

Add 4 to both sides: $$9x - 4 + 4 = 33 + 4$$ , which simplifies to $$9x = 37$$ .