In this page we are going to discuss about **solving inequalities** concept . Math problems contain <,>,<= and >= are called inequalities. Systems of inequalities are a set of two or more inequalities with the same variables. An inequality says that two values are not equal. a ? b says that a is not equal to b for example,

- a < b says that a is less than b.

- a > b says that a is greater than b.

- a ? b means that a is less than or equal to b.

- a ? b means that a is greater than or equal to b.

Related Calculators | |

Calculator for Solving Inequalities | solve compound inequalities calculator |

Solve Inequality Calculator | Solve Linear Inequalities Calculator |

Below are the examples on **solving algebra inequalities **-

**Example 1:**

**Solve for**4(x+1) <2x+3

**Sol:**

**Step 1: **It can be written as 4x+4<2x+3. (Subtract 2x on both the sides)

**Step 2**: 4x+4-2x<2x-2x+3.

**Step 3:**2x+4<3 (subtract 4 on both the sides)

**Step 4**:* *2x+4-4<3-4.

**Step 5: **2x<-1 .so **x= -1/2.**

**Example 2:**

**Solve for ** (4x+2) (10-20x)>=0

**Solution:**

**Step 1: **It can be written as (4x+2)>=0, (10-20x)>=0.

**Step 2:** Now we need to solve x

**Step 3:*** So 4x>=-2, 10-20x>=0. *

**Step 4: **4x>=-2,-20x>=-10.

**Step 5: x>= -2/4, x>=-10/20.**

** Step 6 :** So, the value of x<= 1/2, x<= 1/2.

**Example 3: **

**Solve for **2x^{2}<32

**Solution:**

**Step 1:** Divide using 2 on both the sides

**Step 2:** *2:*x^{2}<16

**Step 3: **It can be written as x

**Step 4:** So **x= 4.**

**Example 4: **

**Solve for ****9x-72 >0.**

**Solution:**

**Step 1: **Here also we need to solve x.

**Step 2:** So, 9x >72.

**Step 3: **Now we need to divide using 9 on both the sides.

**Step 4:** When we divide we get x>8.

Below are the examples on **solving inequalities word problems -**

**Given: **

Suppose a bangle cost 19a earrings14.Write an inequality to find how many earrings you can buy along with one bangle if you have $65to spend.

**Sol:**

**Step 1:** the earrings cost & 14 each .so the total cost will be 14*#of earrings(x).

**Step 2:*** *Cost of 1 bangle + (14 #of earrings) must be $65.

**Step 3:** So it can be written as 19+14x to 65

**Step 4:**14x 65-19

**Step 5:** so the equation is **14x 46.**