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

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.

Answer 2

Answer:

$x<\frac{13}{6}$ and $(-\infty,\frac{13}{6})$.

Step-by-step 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.

$\frac{-12x}{-12}<\frac{-26}{-12}$

$x<\frac{13}{6}$

Therefore, the solution for our given inequality is $x<\frac{13}{6}$ and $(-\infty,\frac{13}{6})$ interval notation.