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
First of all, the first problem makes nonsense. The second condtion is three is less than six. Duh, that has been true a long, long time. All you have is x is greater than -6
Second,
divide by minus three
x>2 or x<-7
Third
x>2x+3
x<-3 Check that
or the second condition add 2x to both sides and add ten to both sides, then divide by 2.
It helps when you state what difficulty you are having
Sure! Let's go through each inequality step by step:
Inequality 1: -6 < x and 3 < 6
To solve this, we have two conditions connected by the "and" operator.
Condition 1: -6 < x
Since the inequality sign is already oriented towards the larger side, we don't need to do anything with it. This condition simply states that x must be greater than -6.
Condition 2: 3 < 6
This condition is a simple comparison, stating that 3 is less than 6. It's always true, regardless of the value of x.
Combining both conditions, we conclude that x must be greater than -6.
Inequality 2: -3x < -6 or x + 5 < -2
To solve this, we have two inequalities connected by the "or" operator.
Inequality 1: -3x < -6
We can solve this inequality by dividing both sides by -3. Remember, when you divide by a negative number, you need to flip the inequality sign:
-3x/-3 > -6/-3
x > 2
Inequality 2: x + 5 < -2
We can solve this inequality by subtracting 5 from both sides:
x + 5 - 5 < -2 - 5
x < -7
Combining both inequalities, we have two possible solutions: x > 2 or x < -7.
Inequality 3: x - 2 > 2x + 1 or -10 > -2x - 2
To solve this, we have two inequalities connected by the "or" operator.
Inequality 1: x - 2 > 2x + 1
To solve this inequality, we can subtract x from both sides and add 2 to both sides to isolate the x term:
x - x - 2 > 2x - x + 1 - 2
-2 > x
Inequality 2: -10 > -2x - 2
To solve this inequality, we can add 2x to both sides and add 10 to both sides to isolate the x term:
-10 + 2x + 2 > -2x + 2x + 10 - 2
2x + 12 > 0
Dividing both sides by 2 gives us:
x + 6 > 0
x > -6
Combining both inequalities, we have two possible solutions: x < -2 or x > -6.
Remember, when solving inequalities, pay attention to signs and remember to reverse the inequality when dividing or multiplying by a negative number.