Can someone show me how to solve these inequalties for me?
I cannot figure any of them out
-6 < x and 3 < 6 (Remember this is an "and" statement)
-3x < -6 or x + 5 < -2
x - 2 > 2x + 1 or -10 > -2x - 2
Sure! I'll walk you through the process of solving each inequality step by step.
1) -6 < x and 3 < 6:
To solve this inequality, we need to find the values of x that satisfy both conditions.
First, let's start with -6 < x. To isolate x, we can add 6 to both sides of the inequality:
-6 + 6 < x + 6
0 < x + 6
Now, let's move on to the second condition, 3 < 6. This condition is already true.
Since we have an "and" statement, we need to find the values of x that satisfy both 0 < x + 6 and 3 < 6.
Since 0 is less than any positive value of x, the first inequality, 0 < x + 6, is satisfied for all values of x. However, we also need to make sure that x satisfies the second condition, which is 3 < 6. Since 3 is indeed less than 6, this condition is also satisfied for all values of x.
Therefore, the solution for this inequality is all real numbers.
2) -3x < -6 or x + 5 < -2:
To solve this inequality, we'll tackle each part separately.
Let's start with -3x < -6. To isolate x, divide both sides of the inequality by -3. Remember that when you divide or multiply an inequality by a negative number, you must flip the inequality sign:
-3x / -3 > -6 / -3
x > 2
Now let's move to the second part, x + 5 < -2. To isolate x, subtract 5 from both sides of the inequality:
x + 5 - 5 < -2 - 5
x < -7
Since we have an "or" statement, the solution to this inequality is the combination of the solutions to each part. Therefore, the solution is x > 2 or x < -7.
3) x - 2 > 2x + 1 or -10 > -2x - 2:
Let's solve each part separately.
Start with x - 2 > 2x + 1. To solve for x, we'll isolate the x term. First, subtract x from both sides of the inequality:
x - 2 - x > 2x - x + 1
-2 > x + 1
Now, move on to the second part, -10 > -2x - 2. To solve for x, we'll isolate the x term again. Add 2 to both sides of the inequality:
-10 + 2 > -2x - 2 + 2
-8 > -2x
To simplify further, divide both sides of the inequality by -2. Remember to flip the inequality sign when dividing by a negative number:
-8 / -2 < -2x / -2
4 < x
Since we have an "or" statement, the solution to this inequality is the combination of the solutions to each part. Therefore, the solution is -8 > x or x > 4.