Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
3. Function Notation
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Exercise 42 Page 126

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

Solution Set: v≤2
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.
4v+9 ≤ 5
4v+9- 9 ≤ 5- 9
4v ≤ -4
4v/4 ≤ -4/4
4/4 * v ≤ -4/4
4/4 * v ≤ -4/4
1 * v ≤ -1
v≤-1
This inequality 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.
-3v ≥ -6
-3v/-3 ≤ -6/-3
3v/3 ≤ 6/3
3/3 * v ≤ 6/3
1 * v ≤ 6/3
v ≤ 6/3
v ≤ 2
This inequality tells us that all values less than or equal to 2 will satisfy the inequality.

Note that the point on 2 is closed because it is included in the solution set.

Compound Inequality

The solution to the compound inequality is the combination of the solution sets. First Solution Set:& v≤ -1 Second Solution Set:& v≤2 Combined Solution Set:& v≤2 Finally, we will graph the solution set to the compound inequality. The union of these solution sets is v ≤ 2.