What is the difference between an equation and an expression? Include an example of each. Can you solve for a variable in an expression? Explain. Can you solve for a variable in an equation? Explain. Write a mathematical phrase or sentence for your classmates to translate. help
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An equation is a mathematical statement that indicates that two expressions are equal. It contains an equal sign (=) and often includes variables that are unknowns or can have different values. An expression, on the other hand, represents a mathematical phrase or a combination of numbers, symbols, and variables, but it does not include an equal sign and does not make a statement of equality.
Example of an equation: 2x + 3 = 9. In this equation, the left side (2x + 3) is equal to the right side (9), indicating that the two expressions are equal.
Example of an expression: 3x - 7. This expression consists of numbers (3, -7) and a variable (x), but there is no equal sign, so it does not make a statement of equality.
In an expression, you can simplify or evaluate it by replacing the variable(s) with specific values and performing the indicated calculations. However, you cannot directly solve for a variable in an expression since there is no equality to solve for.
In contrast, in an equation, you can solve for a variable by performing algebraic operations to isolate the variable on one side of the equation. The goal is to simplify the equation until you have the variable alone on one side of the equal sign. The solution to the equation would be the value(s) of the variable that makes the equation true.
For example, in the equation 2x + 3 = 9, you can solve for x by subtracting 3 from both sides of the equation: 2x = 6. Then, divide both sides by 2: x = 3. So, the solution to the equation is x = 3.
A mathematical phrase/sentence for translation: "The sum of a number and four is equal to twice the number."