1. Combine like terms to simplify the expression.
5x + 4 + 2x + 5 .
2. Use the distributive property to factor the expression.
2k + 10 .
I am really confused on these two questions. Can someone help me out?
5x + 4 + 2x + 5
= 5x + 2x + 4 + 5
= 7x + 9
2k + 10
can you think of a number that will divide evenly into 2k and into 10?
Is it 5?
Sure! I can help you with that. Let's break down each question step by step.
1. Combine like terms to simplify the expression:
To combine like terms, look for terms that have the same variable and exponent. In this case, the like terms are 5x and 2x. The constant terms are 4 and 5. To simplify the expression, add the coefficients of the like terms and keep the variable term unchanged. The constant terms can also be added together.
5x + 4 + 2x + 5
Combine like terms: 5x + 2x = 7x
Combine constant terms: 4 + 5 = 9
The simplified expression is 7x + 9.
2. Use the distributive property to factor the expression:
The distributive property states that for any real numbers a, b, and c, the equation a(b + c) is equal to ab + ac.
In this case, the expression is 2k + 10. To factor it using the distributive property, we have to break it down into two terms and then multiply.
2k + 10 can be written as 2(k + 5)
This means that k + 5 is the common term that can be factored out.
The factored expression is 2(k + 5).
I hope this helps! Let me know if you have any further questions.
Of course! I can help you with these questions.
1. To combine like terms and simplify the expression 5x + 4 + 2x + 5, we need to group the terms with the same variable together. First, let's group the terms with x together: 5x + 2x. This simplifies to 7x. Then we group the constant terms together: 4 + 5. This simplifies to 9. Now we can combine the simplified terms: 7x + 9. Therefore, the expression 5x + 4 + 2x + 5 simplifies to 7x + 9.
2. To factor the expression 2k + 10 using the distributive property, we need to find a common factor that can be multiplied to both terms. In this case, the common factor is 2. We can rewrite the expression as: 2(k + 5). Therefore, using the distributive property, we have factored the expression as 2(k + 5).
I hope this helps! Let me know if you have any further questions.