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,
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Below are the examples on solving algebra inequalities -
Solve for4(x+1) <2x+3
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.
Solve for (4x+2) (10-20x)>=0
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.
Solve for 2x2<32
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.
Solve for 9x-72 >0.
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 -
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.
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.