An equality is a mathematical statement which states that two expressions are not equal. Solving a system of equations or inequalities means finding the set of all ordered pairs of numbers that makes each equation or inequality true. A linear inequality contains linear expressions on one or both sides of the inequality. The inequality is expressed by four different symbols **>, < , ≥, ≤ **. An inequality is the same as an equation except it can have a less than sign, a greater than sign, a less than or equal to sign, or a greater than equal to sign. The solution set of an inequality is the set of numbers that make the inequality true.

- If a,b and c are real numbers and
**if a > b, then a + c > b + c.** - If a,b and c are real numbers and
**if a > b, then a - c > b - c.** - For real numbers a, b, c and c > 0,
**if a > b, then ac > bc.** - For real numbers a, b, c and c < 0,
**if a > b, then ac < bc.** - For real numbers a, b, c and c > 0,
**if a > b, then $\frac{a}{c} > \frac{b}{c}$.** - For real numbers a, b, c and c < 0
**, if a > b, then $\frac{a}{c} < \frac{b}{c}$**.

Step 1:

10x - 5 = 15

Add 5 to each side

=> 10x - 5 + 5 = 15 + 5

Step 2:

Divide each side by 10

=> 10x = 20

=> x = 2

10x - 5 = 15

Add 5 to each side

=> 10x - 5 + 5 = 15 + 5

Step 2:

Divide each side by 10

=> 10x = 20

=> x = 2

Step 1:

5x - 2 $\leq $ 3

Add 2 to each side to eliminate -2 from the left side.

=> 5x - 2 + 2 $\leq $ 3 + 2

=> 5x $\leq $ 5

Step 2:

Divide each side by 5

=> $\frac{5x}{5}\leq \frac{5}{5}$

=>** x $\leq $ 1 **

The solution can be given in interval form and also shown on the number line.

=>The solution as an interval is (-$\infty$,1] .

Step 3:

The solution on the number line is:

5x - 2 $\leq $ 3

Add 2 to each side to eliminate -2 from the left side.

=> 5x - 2 + 2 $\leq $ 3 + 2

=> 5x $\leq $ 5

Step 2:

Divide each side by 5

=> $\frac{5x}{5}\leq \frac{5}{5}$

=>

The solution can be given in interval form and also shown on the number line.

=>The solution as an interval is (-$\infty$,1] .

Step 3:

The solution on the number line is:

Step 1:

First let us remove 10 on the left side

Subtract 10 from each side

4a + 10 - 10 < 6a + 12 - 10

=> 4a < 6a + 2

Step 2:

Subtract 6a from each side

=> 4a - 6a < 6a - 6a + 2

=> - 2a < 2

Dividing the inequality by -2, turns the inequality around as

=> a > -1

The solution as an interval is (-1, ∞)

Step 3:

The solution is shown on number line as follows:

First let us remove 10 on the left side

Subtract 10 from each side

4a + 10 - 10 < 6a + 12 - 10

=> 4a < 6a + 2

Step 2:

Subtract 6a from each side

=> 4a - 6a < 6a - 6a + 2

=> - 2a < 2

Dividing the inequality by -2, turns the inequality around as

=> a > -1

The solution as an interval is (-1, ∞)

Step 3:

The solution is shown on number line as follows:

Step 1:

-4 + 10x = 36

Add 4 to each side

-4 + 10x + 4 = 36 + 4

=> 10x = 40

Step 2:

Divide each side by 10

=> $\frac{10x}{10} = \frac{40}{10}$

=> x = 4, is the answer.

-4 + 10x = 36

Add 4 to each side

-4 + 10x + 4 = 36 + 4

=> 10x = 40

Step 2:

Divide each side by 10

=> $\frac{10x}{10} = \frac{40}{10}$

=> x = 4, is the answer.