Solve each compound inequality.
-1-10a<-1v10+3a< or = -5
-1-10a < -1 or 10+3a <= -5
-10a < 0 or 3a <= -15
a > 0 or a <= -5
To solve each compound inequality, we will break it down into two separate inequalities and solve each one individually.
1) -1 - 10a < -1v10 + 3a
To simplify this inequality, let's first isolate the terms containing 'a' on one side.
-10a - 3a < -1v10 + 1
Combining like terms:
-13a < 10
Now, divide both sides of the inequality by -13, remembering to reverse the inequality symbol since we are dividing by a negative number:
a > 10/-13 (Note: when you divide by a negative number, the inequality sign flips)
Simplifying:
a > -10/13
2) -1v10 + 3a < or = -5
To simplify this inequality, let's first isolate the terms containing 'a' on one side.
3a ≤ -1v10 - 5
Combining like terms:
3a ≤ 10 - 6
Simplifying:
3a ≤ 4
Finally, divide both sides of the inequality by 3 to solve for 'a':
a ≤ 4/3
Therefore, the solutions to the compound inequality are:
a > -10/13 AND a ≤ 4/3