Key takeaway: An equation is a statement that two expressions have the same value, joined by an equal sign, and a solution is any number that makes the statement true.
Grade 66.EE.B.5Expressions and Equations
Definition of Equation
An equation says that two quantities are exactly the same. It has an equal sign with an expression on each side, like \(5x – 8 = 27\). Think of a balance scale that is perfectly level: whatever sits on the left weighs the same as what sits on the right.
When an equation contains a variable, it may be true for some numbers and false for others. A value that makes it true is a solution. To test a candidate, substitute it for the letter and compute both sides. If the results match, the number is a solution; if not, it is not. An equation without a variable, such as \(3 + 4 = 7\), is simply true or false.
Formula and notation
The general shape is
\[\text{left expression} = \text{right expression}\]
The equal sign means “has the same value as”. For example, in \(5x – 8 = 27\) the left side is \(5x – 8\) and the right side is 27. A solution is written as \(x = 7\).
Key facts
- The equal sign is a statement of balance, not an instruction to compute.
- A solution makes both sides equal after substitution.
- Doing the same operation to both sides keeps the statement balanced.
- Some equations have one solution, some none, and some every number.
Equation example
Is \(x = 7\) a solution of \(5x – 8 = 27\)? Is \(x = 6\)?
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Substitute 7 on the left: \(5 \times 7 – 8 = 35 – 8 = 27\). The right side is 27, so both sides match.
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Substitute 6: \(5 \times 6 – 8 = 30 – 8 = 22\). The right side is 27, and \(22 \neq 27\).
Yes, \(x = 7\) is a solution; \(x = 6\) is not.
Common mistake
Watch out
Lila writes \(3 + 4 = 7 + 2 = 9\) to show her work.
Why it is wrong
She treats the equal sign as “and then the answer is”. The string says \(3 + 4 = 9\), which is false. Each equal sign must join two quantities with the same value, so write the steps on separate lines: \(3 + 4 = 7\), then \(7 + 2 = 9\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Expressions and Equations