What is the inequality of "x - 2 > 2x + 1 or 10 > -2x + 2" ?

Question

please show steps so i can understand it better

Answer 1

X - 2 > 2X +1
-2 -1 > 2X - X
-3 > X
so X < -3


10 > -2X + 2
10 - 2 > -2X
8 > -2X
4 > -X
so, X > -4

For inequalities, when u multiply by -1, change the sign of inequality
To verify, you can plug in some values. Always take intervals of X > 0, X = 0, X between 0 and the negative number on the other side of the inequality, X = the other number, and X smaller than the other number.

For example, if 4 > -X then,
if X >0, this will always be true
If -4 < X < 0, then also this wil be true
But if X < = - 4 for example (-5), then this is not true so X must be greater than -4

Answer 2

verify each and each inequality for my area, then integrate outcomes: x - 2 > 2x + a million x - 2x > a million + 2 -x > 3 x < -3 10 > -2x + 2 2x > 2 - 10 2x > -8 x > -4 Now because you're taking income of OR, we get x < -3 or x > -4 yet this contains all actual values of x If, on the distinctive hand, we had x - 2 > 2x + a million AND 10 > -2x + 2, then mixed effect might want to opt to be -4 < x < -3

Answer 3

The first inequality reduces to X < -3 and the second reduces to X < 4. For the second inequality, first subtract 2 from 10 reducing to 8 > -2X. Divide both sides both two , resulting in 4 > -X. Now because of the sign of the unknown random variable is negative divide both sides by -1 and change the direction of the inequality reducing to 4 < X.

Answer 4

This is just an example, you need to understand and do it yourself from now on.

First one
x - 2 > 2x +1

Add 2 on both sides

x > 2x + 3

-3 on both sides

x -3 > 2 x

- x on both sides

- 3 > x solution x < -3

Second

10 > -2x + 2

subtract 2 from both side

8 > -2x

divide both side by -2 , note the arrow direction changed when multiply or divide by a negative number

-4 < x solution x > -4

So the combined answer is x > -4 or x < -3

Answer 5

x - 2 > 2x + 1
+2 +2
x > 2x + 3
-2x>-2x+3
-x > 3 then divide by - and switch sign
x < -3

10 > -2x +2
-2 -2
8 > -2x then divide by -2 and switch sign
-4 < x

Answer 6

'x - 2 > 2x + 1' and '10 > -2x + 2' are the inequalities.
Each of those is called an INEQUALITY (not equal) instead of an EQUATION (notice this means that they ARE EQUAL).

Answer 7

x - 2 > 2x + 1
-x > 3
x < 3

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10 > -2x + 2
10 > -2(x - 1)
-5 < x - 1
x > -4

Answer 8

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