Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
5. Standard Form
Continue to next subchapter

Exercise 74 Page 328

Since the word between the inequalities is or, we are looking for the union of the solution sets to the individual inequalities.

Solution Set: x≤-1 or x>3
Graph:

Practice makes perfect

To solve the compound inequality, we have to solve each of the inequalities separately. Since the word between the individual inequalities is or, the solution set for the compound inequality is the union of the individual solutions.

First Inequality

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign.
5x+3≤-2
5x≤-5
x≤-1
This above tells us that all values less than or equal to -1 will satisfy the inequality.

Note that the point on -1 is closed because it is included in the solution set.

Second Inequality

Again, we will solve the inequality by isolating the variable.
3x+1>10
3x>9
x>3
We found that all values greater than 3 will satisfy the inequality.

Note that the point on 3 is open because it is not included in the solution set.

Compound Inequality

The solution to the compound inequality is the union of the solution sets. First Solution Set:& x≤ -1 Second Solution Set:& x>3 Combined Solution Set:& x≤-1orx>3 Finally, we will graph the solution set to the compound inequality.