Single Variable Equations Sample Problems

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Here are some tips for Single Variable Equations, which aligns with Minnesota state standards:

Single Variable Equations

Important Mastery of this topic is extremely important if you want to do well in algebra. Algebra is all about solving equations for the unknown variable...and it all starts with this topic.

To master this topic, you definitely need to know your basic math facts.
See topics Fast Addition, Fast Subtraction, Fast Multiplication, and Fast Division for review.

Understand these two properties of equality.

Addition Property of Equality
For all rational numbers a, b, and c, if a = b, then a + c = b + c.

Multiplication Property of Equality
For all rational numbers a, b, and c, if a = b, then ac = bc.

When you add the same number to both sides of an equation, you get an equivalent equation.

When you multiply the same number to both sides of an equation, you get an equivalent equation.

To solve for a variable, get the variable on one side and everything else on the other side.
How do we do this?

We "remove" the terms using addition and/or multiplication until the variable is the only term left on one side.

Removing terms by addition:

Removing terms by multiplication:

You can also think about "removing" as using the inverse operation.

Example 1:

Solve.
^-9 = t - 13 t =

So the answer is t =