Solve the inequality and graph the solution. d/2 >2
To solve the inequality:
d/2 > 2
First, we will multiply both sides of the inequality by 2 to eliminate the fraction:
2 * (d/2) > 2 * 2
This simplifies to:
d > 4
Thus, the solution to the inequality is:
d > 4
To graph the solution, we'll plot a solid line at d = 4 on the number line to represent the boundary, and shade the region to the right of 4 since d is greater than 4.
Here is the graph of the solution:
<=======[x------------------>
4
Solve for r. 4≥ r/5
To solve the inequality:
4 ≥ r/5
First, we will multiply both sides of the inequality by 5 to eliminate the fraction:
5 * 4 ≥ 5 * (r/5)
This simplifies to:
20 ≥ r
Thus, the solution to the inequality is:
r ≤ 20
To graph the solution, we'll plot a solid line at r = 20 on the number line to represent the boundary, and shade the region to the left of 20 since r is less than or equal to 20. Here is the graph of the solution:
<-------[-------------------x
20
Solve for d. – 4d≤ – 8
To solve the inequality:
-4d ≤ -8
We will first divide both sides of the inequality by -4. It is important to remember that when dividing by a negative number, the direction of the inequality sign is flipped.
(-4d)/-4 ≥ (-8)/-4
Simplifying this gives:
d ≥ 2
Thus, the solution to the inequality is:
d ≥ 2
To graph the solution, we'll plot a solid line at d = 2 on the number line to represent the boundary, and shade the region to the right of 2 since d is greater than or equal to 2. Here is the graph of the solution:
<=======]-------------x
2
Solve for p. p/2 ≤1.3
To solve the inequality:
p/2 ≤ 1.3
We'll begin by multiplying both sides of the inequality by 2 to eliminate the fraction. Remember that when multiplying or dividing an inequality by a negative number, we must flip the direction of the inequality sign.
2 * (p/2) ≤ 2 * 1.3
This simplifies to:
p ≤ 2.6
Thus, the solution to the inequality is:
p ≤ 2.6
To graph the solution, we'll plot a solid line at p = 2.6 on the number line to represent the boundary, and shade the region to the left of 2.6 since p is less than or equal to 2.6. Here is the graph of the solution:
<-------[--------x
2.6
Solve for f. – 1 f≤ – 3
To solve the inequality:
-1f ≤ -3
Since the coefficient of f is -1, we need to divide both sides of the inequality by -1. Remember that when dividing an inequality by a negative number, the direction of the inequality sign is flipped.
(-1f)/(-1) ≥ (-3)/(-1)
This simplifies to:
f ≥ 3
Thus, the solution to the inequality is:
f ≥ 3
To graph the solution, we'll plot a solid line at f = 3 on the number line to represent the boundary, and shade the region to the right of 3 since f is greater than or equal to 3. Here is the graph of the solution:
<=======]-------------x
3