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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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