Question

1212 times a number xxx, subtracted from 343434, is greater than 8.8.8, point Write an inequality for the statement above. Find the solution set of the inequality. Write the solution using a fraction or integer.

Answer 1

`x<(13)/(6)` and
`(-\infty,(13)/(6))`.

Explanation:

We have been given that 12 times a number x is subtracted from 34, is greater than 0.8.

Let use translate our given statement in an inequality.

12 times a number x would be
`12x`.

We have been given that 12 times a number x is subtracted from 34, so our expression would be:
`34-12x`.

12 times a number x is subtracted from 34, is greater than 0.8. We can represent this information in an inequality as:

`34-12x>8`

Let us solve for x.

`34-34-12x>8-34`

`-12x>-26`

We know that dividing inequality by a negative number flips inequality sign.

`(-12x)/(-12)<(-26)/(-12)`

`x<(13)/(6)`

Therefore, the solution for our given inequality is
`x<(13)/(6)` and
`(-\infty,(13)/(6))` interval notation.

Answer 2

The variable is taken x for unknown number here.

Given statement: 12 times a number x subtracted from 34 is greater than 8.

Times represents multiplication operation.

12 times x = 12*x = 12x.

So, we setup an inequality for above statement as

34 -12x > 8.

Therefore, required inequality is 34 -12x > 8.

Let us solve the inequality for x now.

34 -12x >8

Subtracting 34 from both sides, we get

34-34 -12x > 8-34

-12x > -26.

Dividing both sides by -12, we get

-12x/-12 > -26/-12

x < 13/6. ( Note: on dividing by a negative number, the inequality sign get flip).

So, the solution is x< 13/6.