Lisa B. answered • 05/24/19

Professor Helping Students Succeed in Science, Math for 20+ Years

The key is to translate this problem, one step at a time:

*Write an inequality*

This tells us that we'll use >, <, ≥, or ≤ instead of = when describing the two sides of the equation.

*that represents five less than*

This tells us that we need to take away, or subtract 5: –5

*two times a number*

We don't know the number, so let's call it *x*. Two times *x* is 2*x*.

Then, the previous step tells us we want five less than twice the number, so we say 2*x* –5.

*that is at least fifteen*

"At least fifteen" tells us the first part of the equation can be greater than or equal to 15, which means we need the ≥ sign. If the phrase said "greater than fifteen," we'd use >.

Putting it all together, we get 2*x* – 5 ≥ 15.

*then solve the inequality*

We undo everything the algebra did to *x* to solve in the reverse order.

2*x* – 5 ≥ 15 First, undo the subtraction by adding 5 to both sides.

2*x* ≥ 20 Next, divide both sides by 2.

*x* ≥ 10. We see that x has to be greater than or equal to 10. This means we could pick any number, 10 or greater, and plug it back into the equation we constructed to check our answer.

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