MATH SOLVE

2 months ago

Q:
# 2. Nine more than the opposite of a number is three less than twice the number. What isthe number?

Accepted Solution

A:

Answer:The number is 4Step-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 49 + (-4) = 2 × 4 - 39 - 4 = 8 - 35 = 5The answer is right