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1-3x less than or equal to -2x< 3x+5​

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Answer:

x∈ [1; +∞)

Explanation:

First write down the whole inequality:

1 - 3x ≤ -2 ﹤ 3x + 5

Then it can be seen that there are two separate inequalities here, so we have a system of inequalities:

{1 - 3x ≤ -2,

{3x + 5 ﹥ -2;

we express x from both inequalities:

From the first one:

-3x ≤ -2 - 1

-3x ≤ -3 / : (-3)

x 1

From the second one:

3x ﹥ -2 - 5

3x ﹥ -7 / : 3


x﹥ - (7)/(3)


x﹥ - 2 (1)/(3)

So, now that we have expressed x from both inequalities, we can write down the general range of x values for them (as you can see in the picture, the answer is the common values of x for both inequalities, both red and green colors):

x∈ [1; +∞)

1-3x less than or equal to -2x< 3x+5​-example-1
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