Given below are some examples on solving inequality.

__Example 1:__ Solve x + 4 > 7

**Solution:** We have x + 4 > 7

Using the addition principle for inequality, add -4 to both sides of the given inequality,

x + 4 -4 > 7 - 4

or x > 3.

__Example 2:__ Solve 2x + 5 < 9

**Solution:**

The first priority is to isolate x. For that, subtract 5 from both sides,

2x + 5 - 5 < 9 - 5

or 2x < 4

Divide both sides by 2

$\frac{2x}{2}$ < $\frac{4}{2}$

So, the solution is **x < 2**

__Example 3:__ Solve -4x $\leq$ 3x - 14

**Solution:**

To solve this, we need to isolate x. Subtract 3x from both the sides

-4x - 3x $\leq$ 3x - 14 - 3x

or -7x $\leq$ -14

Divide by 7 on both the sides

$\frac{-7x}{7} \leq \frac{-14}{7}$

**or -x **$\leq$** -2**

Multiply -1 on both sides. This will reverse the inequality sign.

-x (-1) $\geq$ -2(-1)

**or x** $\geq$ **2.**

__Example 4:__

Solve -2x < 4

**Solution: **

Given that -2x < 4

Using multiplication property, multiply both sides of the inequality by -0.5, this reverse the sign,

(-0.5)(-2x) > (0.5) (4)

or x > -2

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