Question

Solve for u. 11–13u>u–6> – 13u–15 Write your answer as a compound inequality with integers, proper fractions, and improper fractions in simplest form.

Answer 1

To solve the compound inequality 11 – 13u > u – 6 > – 13u – 15, we separate it into two separate inequalities and solve each one individually. The solutions are combined to form the compound inequality 9/14 < u < 17/14.

Step-by-step explanation:

To solve the compound inequality 11 – 13u > u – 6 > – 13u – 15, we will separate it into two separate inequalities:

11 – 13u > u – 6

u – 6 > -13u – 15

To solve the first inequality, we will combine like terms and isolate the variable:

11 – 13u > u – 6

11 + 6 > u + 13u

17 > 14u

Divide both sides by 14: 17/14 > 14u/14

u < 17/14

To solve the second inequality, again we combine like terms and isolate the variable:

u – 6 > -13u – 15

u + 13u > -6 + 15

14u > 9

Divide both sides by 14: 14u/14 > 9/14

u > 9/14

Combining the solutions for both inequalities, we get the compound inequality:

9/14 < u < 17/14