Question

The following statement describes the number of marbles, n, in a bag. Ten less than eight times the number of marbles is greater than or equal to the sum of six times the number of marbles and fourteen. Create an inequality to represent this statement, and solve for n. Then, complete the following sentences about the solution.

Answer 1

The number of marbles is greater than or equal to 12.

The inequality would be:

8n-10≥6n+14

We need to gather all of the variables on one side, so we will subtract 6n from both sides:

8n-10-6n≥6n+14-6n
2n-10≥14

Now we will cancel the 10 by adding it:
2n-10+10≥14+10
2n≥24

Divide both sides by 2:
2n/2 ≥ 24/2
n≥12