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Chapter 2: Problem 436

In the following exercises, identify each as an expression or equation. $$ 5 \cdot 8+10 $$

Short Answer

Expert verified
The statement \(5 \times 8 + 10\) is an expression.

Step by step solution

01

Identify the Components

To determine if the given mathematical statement is an expression or an equation, first identify its components. The statement given is:\[ 5 \times 8 + 10 \]
02

Check for Equality Signs

Next, check if the statement contains an equality sign ( = ). An equation always includes an equality sign, indicating that two expressions are equal. In this case, look for an equality sign in \[ 5 \times 8 + 10 \].
03

Draw a Conclusion

Since there is no equality sign ( = ) present in \[ 5 \times 8 + 10 \], the given statement is not comparing two values. Therefore, it is an expression, not an equation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mathematical Expressions
Mathematical expressions are combinations of numbers, variables, and operators (like +, -, *, and /) that represent a value. For example, in the expression \( 5 \times 8 + 10 \), we are performing operations (multiplication and addition) on the numbers 5, 8, and 10.
Unlike equations, expressions do not have an equality sign
They show calculations but don鈥檛 compare two sides; they simply represent a single value.
Remember, if there is no equals sign ( = ), it is always an expression. Here are some more examples:
  • \( 3x + 2 \)
  • \( 7 - 4 \)
  • \( x^2 + 4y \)
Mathematical Equations
Mathematical equations, on the other hand, always include an equality sign ( = ). This sign shows that two expressions are equal to each other. For example, the equation \( 5 \times 8 + 10 = 50 \) declares that the value of the expression on the left (\(5 \times 8 + 10\)) is equal to the value on the right, which is 50.
Equations can be simple or complex, but the key feature is the equality sign.
Some examples include:
  • \( x + 3 = 7 \)
  • \( 2y - 4 = 8 \)
  • \( a^2 + b^2 = c^2 \)
Remember, if there is an equals sign ( = ), it鈥檚 always an equation.
Equality Signs
The equality sign ( = ) plays a crucial role in distinguishing between expressions and equations. It acts as a bridge that tells us that what is on the left side is equal to what is on the right side.
Understanding the Equality Sign:
  • It shows equality between two expressions.
  • Without it, we are simply dealing with an expression, not an equation.
If you don鈥檛 see an equality sign, like in our example \( 5 \times 8 + 10 \), then you are working with a mathematical expression. However, if you see an equality sign, then you have an equation. For instance,
  • \( 3 + 5 = 8 \) is an equation.
  • \( 7 - 2 \) is not an equation, only an expression.

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