What is 5/8x<10?

I would like to have this done by today or so. Thank you!

4 Answers
Feb 22, 2018

The answer is x<16.

Explanation:

You can isolate x by performing the same actions on both sides of the inequality. In this case, first, multiply by 8, then divide by 5.

5/8x<10

5/8xcolor(blue)(*8)<10color(blue)(*8)

5/color(red)cancel(color(black)8)x*color(red)cancel(color(black)8)<10*8

5x<10*8

5x<80

(color(red)cancel(color(black)5)x)/color(red)cancel(color(black)5)<80/5

x<80/5

x<16

This is the solution to the inequality.

Feb 22, 2018

x>1/16

Explanation:

When working with these inequalities, we can treat them as regular algebraic equations when performing operations and moving the variable; however, we need to remember the less than sign:

5/(8x)<10

5<(10)(8x) (Multiply both sides by 8x, this causes 8x to cancel out on the left side)

5<80x

1<(80/5)x (Divide both sides by 5, this causes 5 to cancel out on the left side)

1<16x (Simplify)

1/16<x (Divide both sides by 16. This causes 16 to cancel out on the right side)

If 1/16 is less than x, x must be greater than 1/16. This is why we must remember the sign.
x>1/16

Feb 22, 2018

x < 16

Explanation:

As opposed to the algebraic equations you may be used to dealing with, an inequality instead describes a range of possible values for x.

If x < 3, x could be 2, or -1, or even -pi because all of these values for x satisfy the condition that x must be less than 3.

color(red)(5/8)x < 10

Much like an equation, you can perform identical actions to both sides of the inequality. The sole difference is that when multiplying or dividing by a negative number, the sign swaps. This is best illustrated with an example.

3 < 5, but -3 > - 5

Essentially, multiplying or dividing by a negative number flips the number line, in a sense.

x < 10 * color(red)(8/5)

x < 16

Feb 22, 2018

See below for an explanation:

Explanation:

The equation is 5/8x<10

Multiply 8/5 to both sides:

8/5*5/8x<10*8/5=>

cancel(8/5*5/8)x<16

x<16

The reason why I multiplied 8/5 is that when multiplying a number with its reciprocal, it gives you 1, enabling you to get the answer.