Question

What is 5/8x<10?

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

Answer 1

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.

Answer 2

`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`

Answer 3

`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`

Answer 4

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.