Write an algebraic expression for each of the following verbal phrases.
_______________ 6) eleven times the sum of twelve and five times x
_______________ 9) the product of eight and x increased by fifteen
_______________ 10) four less than the quotient of t and seven
I will do one of them, you do the other two and let us know what you got
9)the product of eight and x increased by fifteen
product ---- the answer to a multiplication
multiplication of what?? }..of eight and x... , so 8x
increased --- means something was added
what was added ? "increased by fifteen" ---- +15
8x + 15
6) 11x+12 (I honestly don't know the rest to this problem. The five times x confuses me)
10) t/7-4
eleven times the sum of twelve and five times x
11(the sum of twelve and five times x)
11(12 + 5x)
What about the last one?
What is a "quotient" ?
A quotient is the answer to a division problem
so
t/7 - 4
or to be absolutely clear about it
(t/7) - 4
To write algebraic expressions for the given verbal phrases, you need to understand and translate the keywords into mathematical symbols. Here's how you can do that:
6) Let's break down the given phrase step by step:
Eleven times: This refers to the multiplication operation, denoted by the symbol "x".
The sum of twelve and five times x: This means you need to add twelve to the product of five and x.
Therefore, the algebraic expression for this verbal phrase is:
11 * (12 + 5x)
9) Let's break down the given phrase step by step:
The product of eight and x: This means you need to multiply eight and x, denoted by 8x.
Increased by fifteen: This means you need to add fifteen to the previous result.
Therefore, the algebraic expression for this verbal phrase is:
8x + 15
10) Let's break down the given phrase step by step:
Four less than: This means you need to subtract four from the following quantity.
The quotient of t and seven: This means you need to divide t by seven, denoted by t/7.
Therefore, the algebraic expression for this verbal phrase is:
(t/7) - 4