solving inequalities for word problems:twice a number plus 10 is greater than three times that number less 4. what is the number?

Accepted Solution

For this case we have to:x: Let the variable representing the unknown numberWe algebraically rewrite the given expression:Twice a number plus 10, is represented as:[tex]2x + 10[/tex]Three times that number less 4. is represented as:[tex]3x-4[/tex]Thus, the complete expression is:[tex]2x + 10> 3x-4[/tex]Subtracting 3x from both sides of the inequality:[tex]2x-3x + 10> -4\\-x + 10> -4[/tex]Subtracting 10 from both sides of the inequality:[tex]-x> -4-10[/tex]Equal signs are added and the same sign is placed:[tex]-x> -14[/tex]We multiply by -1 on both sides, taking into account that the sense of inequality changes:[tex]x <14[/tex]The solution is given by all values of "x" less than 14.Answer:[tex]x <14[/tex]