Question

Enter an inequality that represents the description, and then solve.

Nine more than seven times a number (x) is at least fifty-eight.
Inequality: ?
Solution: x ≥ ?
A) 9+7x≥58;x≥7
B)7x−9≥58;x≥11
C) 7x+9≥58;x≥7
D) 9−7x≥58;x≤−7

Answer 1

To represent the statement 'Nine more than seven times a number is at least fifty-eight' as an inequality, it is written as 7x + 9 ≥ 58. Solving this inequality involves subtracting 9 from both sides and then dividing by 7, resulting in x ≥ 7. The correct option is C.

Step-by-step explanation:

The student's question involves creating and solving an inequality based on a given description. The description is: Nine more than seven times a number (x) is at least fifty-eight. To write this as an inequality, you would express it algebraically. The first step is to translate 'nine more than seven times a number' into an expression, which is 7x + 9. The phrase 'is at least' suggests that the expression should be greater than or equal to a value, which is fifty-eight in this case. Therefore, the inequality is 7x + 9 ≥ 58.

To solve the inequality:

1. Subtract 9 from both sides of the inequality to isolate the term with x. This gives us 7x ≥ 49.
2. Divide both sides by 7 to solve for x. This results in x ≥ 7.

Thus, the correct inequality and solution are:

Inequality: 7x + 9 ≥ 58

Solution: x ≥ 7

Hence, the correct answer is Option C: 7x + 9 ≥ 58; x ≥ 7.