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**Hint:**An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value. Here we need to solve for ‘x’ which is a variable. Solving the given inequality is very like solving equations and we do most of the same thing but we must pay attention to the direction of inequality\[( \leqslant , > )\]. We have two linear inequalities. We can solve this.

**Complete step-by-step solution:**

Given, \[4x - 2 < 6\]

We add 2 on both sides and we know that the inequality direction doesn’t change,

\[

4x - 2 + 2 < 6 + 2 \\

4x < 8 \\

\]

We divide 4 on both sides we have,

\[

x < \dfrac{8}{4} \\

x < 2 \\

\]

Thus the solution of \[4x - 2 < 6\] is \[x < 2\]. The interval form is \[( - \infty ,2)\].

Now take \[3x + 1 > 22\]

Subtract 1 on both sides we have,

\[

3x + 1 - 1 > 22 - 1 \\

3x > 21 \\

\]

Divide by 3 on both sides we have,

\[

x > \dfrac{{21}}{3} \\

x > 7 \\

\]

Thus the solution of \[3x + 1 > 22\] is \[x > 7\]. The interval form is \[(7,\infty )\].

**Note:**We take value of ‘x’ in \[( - \infty ,2)\] and put it in \[4x - 2 < 6\]

Let’s put \[x = 0\] in \[4x - 2 < 6\]

\[ 4(0) - 2 < 6 \\

- 2 < 6 \\

\]

Which is correct. We check for the second inequality in the same way.

We know that \[a \ne b\] says that ‘a’ is not equal to ‘b’. \[a > b\] means that ‘a’ is less than ‘b’. \[a < b\] means that ‘a’ is greater than ‘b’. These two are known as strict inequality. \[a \geqslant b\] means that ‘a’ is less than or equal to ‘b’. \[a \leqslant b\] means that ‘a’ is greater than or equal to ‘b’.

**The direction of inequality do not change in these cases:**

-Add or subtract a number from both sides.

-Multiply or divide both sides by a positive number.

-Simplify a side.

**The direction of the inequality change in these cases:**

-Multiply or divide both sides by a negative number.

-Swapping left and right hand sides.

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