Question

Translate the following statement to an inequality. Then, find the solution. Four times the sum of a number and eight is greater than or equal to negative four.

a. n≥−32
b. n≤−9
c. n≤−32
d. n≥−9

Answer 1

The solution to the inequality derived from the statement 'Four times the sum of a number and eight is greater than or equal to negative four.' is 'n ≥ -9'. It means that 'n' can be any number greater than or equal to -9. The correct answer is d. n ≥ -9.

Step-by-step explanation:

To translate the given statement into an inequality and find the solution, we start with the statement 'Four times the sum of a number and eight is greater than or equal to negative four.' We represent the unknown number with a variable, typically 'n', and set up the inequality accordingly:

4(n + 8) ≥ -4

Next, we solve for 'n' by distributing the 4 and then isolating 'n' on one side of the inequality:

1. Distribute the 4 to both terms inside the parentheses: 4 × n + 4 × 8 ≥ -4
2. Which simplifies to: 4n + 32 ≥ -4
3. Subtract 32 from both sides: 4n ≥ -36
4. Divide both sides by 4: n ≥ -9

Therefore, n ≥ -9 is the correct inequality that represents the given statement. The solution is that 'n' can be any number greater than or equal to -9 (option d).