Checking equation solutions involves substituting a given value for a variable in an equation to see if it makes the equation true. If substituting the value makes both sides of the equation equal, the value is a solution. If not, it isn't. This process helps verify the correctness of solutions you've found and is a fundamental skill in algebra.
For example, let's say we have the equation $x + 3 = 7$. If we want to check if $x = 4$ is a solution, we substitute $4$ for $x$: $4 + 3 = 7$. Since $7 = 7$, the value $x = 4$ is indeed a solution to the equation.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Equation | A. A value that, when substituted for a variable, makes the equation true. |
| 2. Variable | B. A mathematical statement that two expressions are equal. |
| 3. Solution | C. The process of replacing a variable with a given value. |
| 4. Substitute | D. A symbol (usually a letter) that represents an unknown value. |
| 5. Verify | E. To confirm or check the accuracy of a result. |
Match the terms above: 1-B, 2-D, 3-A, 4-C, 5-E
To check if a value is a ________ to an equation, you ________ the value for the ________ in the equation. If both sides of the equation are ________ after the substitution, then the value is a solution.
Fill in the blanks: solution, substitute, variable, equal
Why is it important to check your solutions when solving equations?
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