Can any body help me solve this inequality. How to write the solution on a numberline.
|2x+2|>14
(2x+4) > 14
2x > 10
x > 5
BUT ALSO
-(2x+4)>14
-2 x > 18
- x > 9
now multiply both sides by -1
BUT when you multiply by negative, reverse arrow
x < -9
For the number line, go to
http://www.wolframalpha.com/input/?i=%7C2x%2B2%7C%3E14
and scroll down some.
To solve the inequality |2x + 2| > 14 and represent the solution on a number line, follow these steps:
1. First, remove the absolute value by breaking it into two separate inequalities:
2x + 2 > 14 and -(2x + 2) > 14
2. Solve the first inequality:
2x + 2 > 14
Subtract 2 from both sides: 2x > 14 - 2
Simplify: 2x > 12
Divide both sides by 2 (since the coefficient of x is 2): x > 6
3. Solve the second inequality:
-(2x + 2) > 14
Distribute the negative sign: -2x - 2 > 14
Add 2 to both sides: -2x > 14 + 2
Simplify: -2x > 16
Divide both sides by -2 (remember to flip the inequality sign when dividing by a negative number): x < 8
4. Plot the solutions on a number line:
Mark a point on the number line at 6 (since x > 6) and another point at 8 (since x < 8).
Draw an open circle around each point to indicate that they're not included in the solution (since the inequality is strictly greater than or less than).
Finally, draw an arrow from the open circle at 6 to the left and another arrow from the open circle at 8 to the right to indicate that the solution includes all values between 6 and 8.
So, the solution to the inequality |2x + 2| > 14, represented on a number line, is x < 8 or x > 6.