a Set up the inequalities following the instructions.
B
b Solve the previous inequalities by manipulating them similar to if they were equations.
A
aExample Inequalities:
A x + 5 &< 15
B x - 2 &≤ 4
C x + 3 &> 12
D x - 4 &≥ 3
B
bSolutions and graphs for the example inequalities:
Practice makes perfect
a We are asked to use the inequality symbols <, ≤ , >, and ≥ to write four inequalities involving addition or subtraction. There is no unique way to do this. There are infinitely many ways to set up inequalities satisfying the given instructions. We will illustrate some examples.
A x + 5 &< 15
B x - 2 &≤ 4
C x + 3 &> 12
D x - 4 &≥ 3
b We are now asked to solve the inequalities we set up in the previous part of the exercise and graph them.
Inequality A
We have the inequality x + 5 < 15. We can solve inequalities in a similar way as equations. We will isolate the variable x by using inverse operations.
As we can see, the solutions for this inequality are all those numbers less than 10. To graph this, we can use an open circle at 10 indicating it is not part of the solution set. Then we will shade the values to left of 10 to indicate that numbers less than 10 are solutions.
Inequality B
We have the inequality x -2 ≤ 4. We will isolate the variable x by using inverse operations.
As we can see, the solutions for this inequality are all those numbers less than or equal to 6. To graph this, we can use a closed circle at 6 indicating it is part of the solution set. Then we will shade the values to left of 6 to indicate that numbers less than 6 are solutions as well.
Inequality C
Inequality C is x + 3 > 12. We can isolate the variable x by using inverse operations.
As we can see, the solutions for this inequality are all those numbers greater than 9. To graph this, we can use an open circle at 9 indicating it is not part of the solution set. Then we will shade the values to right of 9 to indicate that numbers greater than 9 are solutions.
Inequality D
Finally, we have the inequality x -4 ≥ 3. We will isolate the variable x by using inverse operations.
As we can see, the solutions for this inequality are all those numbers greater than or equal to 7. To graph this, we can use a closed circle at 7 indicating it is part of the solution set. Then we will shade the values to right of 7 to indicate that numbers greater than 7 are solutions as well.
