Question

Solving inequalities for word problems:

twice a number plus 10 is greater than three times that number less 4. what is the number?

Answer 1

For this case we have to:

x: Let the variable representing the unknown number

We algebraically rewrite the given expression:

Twice a number plus 10, is represented as:
`2x + 10`

Three times that number less 4. is represented as:

`3x-4`

Thus, the complete expression is:

`2x + 10> 3x-4`

Subtracting 3x from both sides of the inequality:

`2x-3x + 10> -4\\-x + 10> -4`

Subtracting 10 from both sides of the inequality:

`-x> -4-10`

Equal signs are added and the same sign is placed:

`-x> -14`

We multiply by -1 on both sides, taking into account that the sense of inequality changes:

`x <14`

The solution is given by all values of "x" less than 14.

Answer:

`x <14`