Question

can you help?
4 increased by the product of a number and 3 is less than or equal to -23

Answer 1

Since you need to write an inequality, the first step is to choose a variable to represent the unknown number.

Answer 2

\(\sf 4 ~increased ~by ~the ~product ~of \color{red}{~a ~number} ~and ~3 ~is ~less ~than ~or ~equal ~to ~-23.\)

How about we use "x" to represent "a number?"

Answer 3

okay

Answer 4

Ok.
Now we look at the rest of the sentence, piece by piece, and we build up our inequality.

Answer 5

We have this so far:

\(\sf 4 ~increased ~by ~the ~product ~of \color{red}{~a ~number} ~and ~3 ~is ~less \)~than ~or ~equal ~to ~-23.

\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{x}\)

Answer 6

\(\sf 4 ~increased ~by ~\color{green}{the ~product ~of ~a ~number ~and ~3} ~is ~less \)~than ~or ~equal ~to ~-23.

How do we represent the green part now?

Answer 7

idk what to do with the four
i know \[x+3\le23\]

Answer 8

-23

Answer 9

That is not correct.
Stick with me. We will do it one step at a time.
Remember that we already picked x for the number.
Now we need to express the product of the number and 3.
Product is what operation?

Answer 10

multiply..... i think

Answer 11

Correct.
Since product is multiplication, then the product of a number and 3 means 3 times the number.
The number is x.
What is 3 times x?

Answer 12

3x

Answer 13

4+3n<or = -23?

Answer 14

Good.
We have this now:

\(\sf 4 ~increased ~by \color{green}{~the ~product ~of ~a ~number} ~and ~3 ~is ~less~than ~or ~equal ~to ~-23.\)

\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{green}{3x}\)

Answer 15

Now we deal with "increased by 4".

When you increase a number by another number, you add the number. An increase is an addition.

Answer 16

thanks you i got it :)

Answer 17

\(\sf \color{purple}{4 ~increased ~by ~the ~product ~of ~a ~number ~and ~3} ~is ~less~than ~or ~equal ~to ~-23.\)

\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{purple}{4 + 3x}\)

Answer 18

You welcome : if ur talking to me

Answer 19

oh and thx for the medal

Answer 20

Finally we o the end of the sentence.

\(\sf \color{purple}{4 ~increased ~by ~the ~product ~of ~a ~number ~and ~3}\color{red}{ ~is ~less~than ~or ~equal ~to ~-23.}\)

\(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{purple}{4 + 3x}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{red}{\le -23}\)

Answer 21

The final inequality is:

\(3x + 4 \le -23\)

If you need to solve it, then you do this:

Subtract 4 from both sides.

\(3x \le -27\)

Divide both sides by 3:

\(x \le -9\)

Answer 22

thanks you are very helpful though i just needed help writing the equation but i fanned you because i appreciate the break down to help me learn

Answer 23

You're welcome.
You can use the process I showed for other similar problems.
That's why I didn't stop even when you had already been given the answer with no explanation.