Question

Eight more than twice a number is greater than negative sixteen. Find all numbers that make this statement true.

a) -5
b) -4
c) -3
d) -2

Answer 1

To solve the inequality 'eight more than twice a number is greater than negative sixteen', we express it as 2x + 8 > -16, subtract 8 from both sides, then divide by 2, resulting in x > -12. All provided options (-5, -4, -3, -2) satisfy this inequality as they are all greater than -12.

Step-by-step explanation:

The question is asking to solve the inequality eight more than twice a number is greater than negative sixteen. Mathematically, this can be expressed as 2x + 8 > -16. To solve for x, we'll perform the following steps:

1. Subtract 8 from both sides of the inequality to isolate the term with x on one side: 2x > -24.
2. Divide both sides by 2 to solve for x: x > -12.

Now we can compare the options given to see which numbers are greater than -12:

• -5 is greater than -12, so it satisfies the inequality.
• -4 is greater than -12, so it also satisfies the inequality.
• -3 is greater than -12, so it satisfies the inequality as well.
• -2 is greater than -12, so this option satisfies the inequality too.

All options given are numbers that make the original statement true as they are all greater than -12.