Another way to put it is that an expression is not a complete mathematical sentence. So 5 + d is an expression, but 5 + d = 7 is not.
Second, a linear expression is linear. There are no exponents in the expression that are greater than one. Though 5 + d is a linear expression, 5 + d2 is not.
It’s possible to write linear expressions in multiple ways; it depends on what part of the linear expression you want to emphasize. You can also write a linear expression in different ways to help you understand equivalent relationships. That’s particularly useful in looking at the relationships among fractions, decimals, and percentages.
As you work through this lesson, be aware of how you are using your time and how you are meeting your goals. Having the 21st century skill to manage your goals and your time will help you work carefully and efficiently. If you are not sure of a goal, reread the information on the slate. To the extent possible, avoid letting your mind wander. Devoting 100% of your attention to the work at hand can make a difference in how well—and how quickly—you master the material.
In summary, an expression is not a complete mathematical sentence, whereas an equation is. A linear expression does not have exponents greater than one, and it can be written in multiple ways to emphasize different parts or understand equivalent relationships. It is important to manage goals and time effectively while working to improve understanding and efficiency.
To summarize the information given:
- An expression is not a complete mathematical sentence. For example, "5 + d" is an expression, but "5 + d = 7" is not.
- A linear expression is one that does not have exponents greater than one. For example, "5 + d" is a linear expression, but "5 + d^2" is not.
- Linear expressions can be written in different ways to emphasize different parts or to show equivalent relationships.
- Managing goals and time is an important 21st-century skill that can help in working carefully and efficiently.
- Giving 100% attention to the work at hand can improve understanding and speed of mastering the material.
It seems like you have mentioned various concepts related to expressions and linear expressions. Let me clarify them one by one.
Firstly, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that doesn't have an equal sign. For example, "5 + d" is an expression because it contains numbers (5) and a variable (d) combined with addition.
On the other hand, a complete mathematical sentence or equation includes an equal sign. So, "5 + d = 7" is not just an expression but a complete mathematical sentence because it states that the sum of 5 and the variable d is equal to 7.
Secondly, a linear expression is a type of expression that doesn't have exponents greater than one. It means that variables only appear with a power of one (i.e., no squared, cubed, or higher powers). For instance, "5 + d" is a linear expression because the variable d is just raised to the power of one. However, "5 + d^2" is not a linear expression because the variable d has an exponent of 2.
In terms of writing linear expressions in different ways, it depends on what you want to emphasize or the context of the problem. Different forms of linear expressions can help you understand equivalent relationships or solve specific math problems. For example, you might rewrite "5 + d" as "d + 5" to highlight that the order doesn't affect the value of the expression.
Lastly, the paragraph you provided emphasizes the importance of managing your goals and time while studying, as well as staying focused on the task at hand. It suggests that being attentive and dedicated to your work can lead to better understanding and quicker mastery of the material.