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Solving inequalities for word problems:

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

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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

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