Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line.
1. 2(3x + 1)< -10 or 3(2x - 4) ¡Ý 0
The or means union of these inequalities.
2. 5(p + 3) + 4 > p - 1 or 4(p - 1) + 2 > p + 8
What is -3<x-10????
bhluyvku
To solve compound inequalities, you need to solve each inequality separately and then combine their solutions.
1. 2(3x + 1) < -10 or 3(2x - 4) ≥ 0
First, let's solve the first inequality:
2(3x + 1) < -10
6x + 2 < -10
6x < -12
x < -2
Now, let's solve the second inequality:
3(2x - 4) ≥ 0
6x - 12 ≥ 0
6x ≥ 12
x ≥ 2
To combine the solutions, we use the union (∪) symbol. So, the combined solution is x < -2 or x ≥ 2.
Now, let's write the solutions in interval notation. For x < -2, we write it as (-∞, -2). For x ≥ 2, we write it as [2, ∞).
Therefore, the final solution in interval notation is (-∞, -2) ∪ [2, ∞).
To graph the solution on a number line, draw a number line and mark -2 with an open circle (since x is not equal to -2), and shade the line to the left of -2, and from 2 onwards.
font problem with #1
#2:
5(p + 3) + 4 > p - 1 means p > -5
4(p - 1) + 2 > p + 8 means p > 10/3
so p > -5 or p > 10/3 means p > -5