Question

Six added to 3 times a number is equal to 4 less than 5 times the number.

10
5
–5
–10

Answer 1

-5

Answer 2

First, let's write the sentence as an equation.
Then we will solve the equation.
Ok?

Answer 3

Ok

Answer 4

Six added 3 times

Answer 5

"a number" means an unknown number. We need a variable (a letter).
Would you like to use x?

Answer 6

Yes

Answer 7

Ok, we'll use x.
Let's deal with this first:
"Six added to 3 times a number "
The number is x. What is "3 times a number" ?

Answer 8

so it is 3x Right?

Answer 9

Yes.
Next, what is "Six added to 3 times a number "
That means 6 added to 3x.
How do you write that using a + sign?

Answer 10

3x +

Answer 11

Right, but what comes after the +?
You are adding \(\Huge \color{red}{6} \) to the 3x.

Answer 12

So 3x + 6

Answer 13

Great.
Now we have an easy part.
"is equal to" is exactly what the equal sign means, so we use it.
3x + 6 =

Answer 14

Ok

Answer 15

Now we work on the last part:
"4 less than 5 times the number"
"the number" is the same number we are dealing with, so it's still x.
How do you write "5 times the number"?

Answer 16

5x

Answer 17

Great.
Now we need to deal with "4 less"
Remember that less means taking away, which means a subtraction.
4 less than 5x means start with 5x and take away 4.
How would you write it using a subtraction?

Answer 18

5x - 4

Answer 19

Great.
Now we can put the last part we just did together with the first part, and we have an equation.

Answer 20

3x + 6 = 5x - 4

Answer 21

ok

Answer 22

In algebra, this equation represents the problem you were given as a sentence in English.
Now we need to solve our equation to find a solution to the equation.