2. Nine more than the opposite of a number is three less than twice the number. What is

the number?

The number is 4

Step-by-step explanation:

* Lets revise some words in mathematics and how change them to

mathematical symbols

- More than ⇒ add (+)

- Less than ⇒ subtract (-)

- Twice ⇒ Multiplied by 2 ( * 2)

- Opposite of a number ⇒ change its sign (additive inverse of it)

* Now lets solve the problem

- Nine more than the opposite of a number is three less than twice

the number

- Assume that the number is x

∴ 9 more than the opposite of x

- That means find the opposite of x and add it by 9

∵ The opposite of x is - x

∴ Nine more than the opposite of a number = - x + 9

- Three less than twice the number means 3 less than twice x

∵ The number is x

∴ Twice the number = 2 * x = 2x

∵ Three less than twice x = 2x - 3

∴ Three less than twice the number = 2x - 3

- The meaning of "is" between the two the statements is "="

∴ Nine more than the opposite of a number is three less than twice

the number is ⇒ - x + 9 = 2x - 3

* Lets solve the equation to find x

∵ - x + 9 = 2x - 3

- add x in both sides

∴ 9 = 3x - 3

- Add 3 to both sides

∴ 12 = 3x

- Divide both sides by 3

∴ x = 4

∵ x represents the number

∴ The number is 4

* Lets check the answer

9 more than opposite 4 is 3 less than twice 4

9 + (-4) = 2 * 4 - 3

9 - 4 = 8 - 3

5 = 5

The answer is right