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# Solving Inequalities

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

## Solving Algebra Inequalities

Below are the examples on solving algebra inequalities

Example 1:

Solve for4(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 2x2<32

Solution:

Step 1: Divide using 2 on both the sides

Step 2: 2:x2<16

Step 3: It can be written as x2<42

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.

## Solving Inequalities Word Problems

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.

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