Question

Translate into mathematical language and solve: Three times a number minus two is less than 58."

A) 3x - 2 < 58; x < 20
B) 3x - 2 > 58; x > 20
C) 3x - 2 = 58; x = 20
D) 3x - 2 < 58; x > 20

Answer 1

The phrase "Three times a number minus two is less than 58" is translated into the inequality 3x - 2 < 58. Solving this inequality, we find that x must be less than 20.

Step-by-step explanation:

To translate the phrase "Three times a number minus two is less than 58" into mathematical language, we start by representing the unknown number with a variable such as x. Three times a number is written as 3x, and then we subtract two from it, which is written as 3x - 2. Finally, we denote that it is less than 58 by using the symbol <, forming the inequality 3x - 2 < 58.

To solve the inequality, we add 2 to both sides to isolate the term with the variable :

• 3x - 2 + 2 < 58 + 2
• 3x < 60

Next, we divide both sides by 3 to solve for x:

• 3x / 3 < 60 / 3
• x < 20

Therefore, the solution is x < 20, which corresponds to option A.