Equation
In short: Equation is a statement that two expressions have the same value, written with an equals sign, such as x + 7 = 19, which is true only when x is 12.
6th GradeAlgebra6.EE.B.5
What is Equation?
Think of an equation as a balanced scale. The left pan holds one expression, the right pan holds another, and the equals sign claims they weigh the same.
Precisely, an equation like \(x + 7 = 19\) can be true or false depending on the value given to the variable. A value that makes it true is a solution: substituting 12 gives \(12 + 7 = 19\), a true statement, while 10 gives \(17 = 19\), which is false.
How to spot it
- A sentence says “is”, “equals” or “the total is” and gives a result for an unknown amount.
- The equals sign appears with a letter on at least one side.
- You are asked whether a number is a solution, or to find the number that works.
- A balance picture shows two sides that must stay level.
The method
- Write each side as an expression and connect them with an equals sign.
- To test a value, substitute it for the variable on both sides.
- Evaluate each side with the order of operations.
- If the two results match, the value is a solution; if not, try another value or solve.
Equation: solved example
Problem
A soccer club in Phoenix collects $8 per player plus a $30 field fee, for a total of $94. The equation is \(8p + 30 = 94\). Is \(p = 9\) a solution? Is \(p = 8\)?
Solution
Test 9: \(8 \cdot 9 + 30 = 72 + 30 = 102\), which is not 94, so 9 fails.
Test 8: \(8 \cdot 8 + 30 = 64 + 30 = 94\), a match. So \(p = 8\) is the solution: the club has 8 players.
Try it
Question 1
Is \(n = 6\) a solution of \(4n – 5 = 19\)?
Show the answer
\(4 \cdot 6 – 5 = 19\), a true statement, so yes.
Question 2
Write an equation for “a number divided by 5 equals 13” and find the number.
Show the answer
\(\frac{m}{5} = 13\), so \(m = 13 \cdot 5 = 65\).
Equation vs. Algebraic Expression
An equation has an equals sign and makes a claim that can be true or false. An expression has no equals sign and is only a phrase with a value. Solving works on equations; evaluating and simplifying work on expressions.
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Whole dictionary: A–Z · 6th Grade · Algebra