Can someone shwo me how to solve these inequalties for me?
3. -6 < x and 3 < 6 (Remember this is an "and" statement)
4. -3x < -6 or x + 5 < -2
5. x - 2 > 2x + 1 or -10 > -2x - 2
Of course! I can explain how to solve these inequalities step by step.
3. -6 < x and 3 < 6 (Remember this is an "and" statement)
To solve this inequality, you need to find the values of x that satisfy both conditions. Let's begin with the first condition: -6 < x. This means that x must be greater than -6.
Next, let's look at the second condition: 3 < 6. This is a true statement, but it doesn't really provide any additional information in this case.
Since we have an "and" statement, we need to find the intersection of the two conditions. In this case, since x must be greater than -6 and there are no other restrictions, we can conclude that x can take any value greater than -6.
Therefore, the solution to this inequality is x > -6.
4. -3x < -6 or x + 5 < -2
Let's solve each inequality separately:
First inequality: -3x < -6
To solve this, divide both sides by -3. Remember that dividing or multiplying both sides of an inequality by a negative number requires flipping the inequality sign.
Dividing both sides by -3 gives us x > 2.
Second inequality: x + 5 < -2
To solve this, subtract 5 from both sides:
x < -7.
Since we have an "or" statement, we need to find the union of the two solutions. In this case, the solution is any value of x that is greater than 2 or less than -7.
Therefore, the solution to this inequality is x > 2 or x < -7.
5. x - 2 > 2x + 1 or -10 > -2x - 2
Let's solve each inequality separately:
First inequality: x - 2 > 2x + 1
To solve this, subtract x from both sides and subtract 1 from both sides:
-2 > x + 1
Subtract 1 from both sides once more:
-3 > x
Second inequality: -10 > -2x - 2
To solve this, add 2 to both sides and divide both sides by -2. Remember to flip the inequality sign when dividing or multiplying by a negative number:
4 < x
Since we have an "or" statement, we need to find the union of the two solutions. In this case, the solution is any value of x that is less than -3 or greater than 4.
Therefore, the solution to this inequality is x < -3 or x > 4.