Answer: The expression derived shall be
A - 8(2A+ 5)
Step-by-step explanation: First of all, let us call the unknown number ‘A.’
Looking at the expression from the latter part of it, we have “...the sum of twice the number and five...,”
This can be written as the sum of 2 x A and 5, that is 2A + 5. Then earlier the question states that the unknown number A, is decreased by 8 times the expression we just came up with. In other words, A is decreased by 8 times 2A + 5. So what we now have is,
A minus 8 times 2A + 5 which can be re-written as
A - 8(2A + 5)
Answer:
[tex]-15x-40[/tex]
Step-by-step explanation:
I have always had a hard time with these problems but after much practice I have mastered it. Just keep practicing these problems and you can master it to. I will help you under stand how to solve this problem one step at a time.
I will bold important key words you need to look out for
So: The problem reads " a number is decreased by eight times the sum of twice the number and five."
In word problems like this one, when it says "a number" that usually means an unknown number. That unknown number is any variable. I usually use x for the unknown number.
Here are the steps to decode what this problem is asking us to make
Step 1. "a number" That number will be X
[tex]x[/tex]
Step 2. "decreased" decreased usually means a subtraction sign
[tex]x-[/tex]
Step 3. "by eight" so the number being used to subtract is the number 8
[tex]x-8[/tex]
Step 4. "times" This means there will be multiplication. The use of parenthesis in math indicates multiplication.
[tex]x-8()[/tex]
Step 5. "the sum" The sum is the key word for addition. This will be inside the parenthesis. Two number will be added together.
[tex]x-8(+)[/tex]
Step 6. "twice the number" This means the value of 2 is multiplying with an unknown number. Like we said earlier, an unknown number is the value of x.
[tex]x-8(2x+)[/tex]
Step 7. "and five" This just means the number 5.
[tex]x-8(2x+5)[/tex]
The two numbers that will be added together is 2x and 5. That is the sum. So, in other words, it is "the sum of twice the number and five."
The equation we form is [tex]x-8(2x+5)[/tex] but this is not in it's simplest form.
Step 8. We need to distribute 8 into both numbers inside the parenthesis.
[tex](-8 * 2x)[/tex] and [tex](-8 * 5)[/tex]
[tex](-8 * 2x) = -16x[/tex] and [tex](-8 * 5) = -40[/tex]
So we are left with: [tex]x-16x-40[/tex]
Step 9. We need to combine like terms. The only like terms here are x and -16x
[tex](x-16x) = -15x[/tex]
So we are left with: [tex]-15x-40[/tex]
There is no equal sign in this word problem so this will be your final and simplified answer. If there was an equal sign you can further simplify the problem by getting x by itself and finding the value of x.
I will upload a picture of how to distribute if you do not understand the text.
