can someone SHOW me how to solve these graphs?2x > -6 and x - 4 < 3
x + 5 > 2x + 1 and -4x < -8
-6 < x + 3 < 6 (Remember this is an "and" statement)
-3x < -6 or x + 5 < -2
x - 2 > 2x + 1 or -10 > -2x - 2
Look at the third.
-6 < x + 3 < 6 (Remember this is an "and" statement)
so x+3 is greater than -6, or
x is greater than -3. So to the right of -3 is allowed, but we have a second conditon: x+3 is les than six. or x is less than 3.
so the allowed solution is between -3 and 3.
I will be happy to critique your thinking on the others.
Look at the third.
-6 < x + 3 < 6 (Remember this is an "and" statement)
so x+3 is greater than -6, or
x is greater than -3. So to the right of -3 is allowed, but we have a second conditon: x+3 is les than six. or x is less than 3.
so the allowed solution is between -3 and 3.
I will be happy to critique your thinking on the others.
Sure! Let's go through the other equations step by step.
For the first equation:
2x > -6
To solve this inequality, we need to isolate x on one side of the inequality symbol. To do this, we divide both sides by 2 (remembering to reverse the inequality if we divide by a negative number):
2x/2 > -6/2
x > -3
So the solution to this equation is x is greater than -3.
For the second equation:
x - 4 < 3
To solve this inequality, we add 4 to both sides of the inequality:
x - 4 + 4 < 3 + 4
x < 7
So the solution to this equation is x is less than 7.
Now let's move on to the fourth equation:
-3x < -6 or x + 5 < -2
This is a compound inequality with an "or" statement. We can solve each part separately.
For the first part, -3x < -6:
To isolate x, we divide both sides by -3 (remembering to reverse the inequality):
-3x/(-3) > -6/(-3)
x > 2
So the solution to the first part of the equation is x is greater than 2.
For the second part, x + 5 < -2:
We subtract 5 from both sides of the inequality:
x + 5 - 5 < -2 - 5
x < -7
So the solution to the second part of the equation is x is less than -7.
Now let's move on to the last equation:
x - 2 > 2x + 1 or -10 > -2x - 2
This is another compound inequality with an "or" statement. We can solve each part separately.
For the first part, x - 2 > 2x + 1:
To isolate x, we subtract 2x from both sides:
x - 2 - 2x > 2x + 1 - 2x
-x - 2 > 1
Next, we add 2 to both sides:
-x - 2 + 2 > 1 + 2
-x > 3
Finally, we multiply both sides by -1 (remembering to reverse the inequality):
x < -3
So the solution to the first part of the equation is x is less than -3.
For the second part, -10 > -2x - 2:
To isolate x, we add 2x to both sides:
-10 + 2x > -2x - 2 + 2x
2x > -12
Then, we divide both sides by 2:
2x/2 > -12/2
x > -6
So the solution to the second part of the equation is x is greater than -6.
Now we have two solutions: x is less than -3 or x is greater than -6.
I hope this helps! Let me know if you have any further questions.