X - 2 > 2x + 1 or 10 > -2x + 2

Question

can you help me solve this problem please.. im supposed to graph but i just need the equation....

x - 2 > 2x + 1 or 10 > -2x + 2

Answer 1

for = x - 2 > 2x + 1

x - 2 > 2x + 1

-x        -x

_________________

-2 > 1x + 1

-1            -1

__________________

-3 > 1x

--     ---

1       1

the answer = -3 < x

Answer 2

x-2>2x+1

-x>3

x<-3

10>-2x+2

8>-2x

-4<x

Answer 3

x > 2x + 3  or  8 > -2x

Broken down furthur (if needed):

1/2x > 3   or  -4 > x

Answer 4

You need to graph all the values that satisfy two inequalities:

1)  x - 2 > 2x + 1

-or-

2)  10 > -2x + 2

First, let's solve for the first inequality:

x - 2 > 2x + 1

x > 2x + 3

0 > x + 3

-3 > x

x < -3

If your graph this inequality, it would be represented by a dashed vertical line that is parallel to the Y axis and runs up and down at -3 on the X axis.  Then, all the area to the LEFT of the dashed line would be shaded because that area is where X is < -3.

Next, you need to solve the second inequality:

10 > -2x + 2

2x + 10 > 2

2x > -8

x > -4

If your graph this inequality, it would be represented by a dashed vertical line that is parallel to the Y axis and runs up and down at -4 on the X axis.  Then, all the area to the RIGHT of the dashed line would be shaded because that area is where X is > -4.

If you really are solving this as a pair of inequalities and want all the values that satisfy either of them, then, you must take every area on the combined graph that has any shading because of the word OR in your original question that links the two inequalities.  When you combine these two graphs, the entire graph area would have some shading. So, EVERY NUMBER satisfies this pair of inequalities.

If the word in your question linking the two inequalities is AND, then you must take only the shaded area that is common to both inequalities.  In this case, the common area for both graphs is all the area between -3 and -4 on the X axis.  If the inequalities are combined with AND an expression of the combined area would be written:

-4 < x < -3

Does this help?