One-fifth of the sum of 16 and a number is at least 10.

Question

inequalties and word problem. need help with a word problem

Answer 1

≥It's important to take word problems step by step! When you see the word "of" in a word problem it always means you are multiplying. Sum means addition. Knowing this, we can complete the left side of the equation. 

 

1/5*(16+x)

 

now, for the sign! It says the left side is AT LEAST 10. That means it can be GREATER THAN 10. however, the number could also be 10, so we will use the sign for greater than or equal to. So we can now complete the rest of the equation. 

 

1/5*(16+x)≥10

 

Now, solve for x. First, multiply both sides by 5. This will make the 1/5 on the left side cancel. 

 

(16+x)≥50

 

now subtract 16 from both sides.

 

X≥34

 

so x is any number greater than or equal to 34. 

Answer 2

(1/5)·(16+x) ≥ 10

 

Solve with the same steps as solving an equation:

Multiply both sides by 5 to clear the fraction.

    16+x ≥ 50

 

Subtract 16 from both sides:

         x ≥ 34

 

So, the number is at least 34.