# INVERSE OPERATIONS

Inverse operations are opposite operations. That is, one reverses the effect of the other.

• Addition and subtraction are inverse operations
• Multiplication and division are inverse operations  In solving problems in algebra, we use inverse operations to isolate the given variable.

## Examples

Example 1 :

Solve for k :

7k  =  35

Solution :

Here 7 and k are multiplied.

So, we have to use the inverse operation of multiplication to solve for k.

Inverse operation of multiplication is division.

7k  =  35

Divide both sides by 7.

k = 5

Example 2 :

Solve for k ;

k + 7  =  9

Solution :

Here 7 is added to k.

So, we have to use the inverse operation of addition to solve for k.

Inverse operation of addition is subtraction.

k + 7  =  9

Subtract 7 from each side.

k  =  2

Example 3 :

Solve for b :

b/8  =  7

Solution :

Here b is divided by 8.

So, we have to use the inverse operation of division to solve for b.

Inverse operation of division is multiplication.

b/8  =  7

Multiply each side by 8.

b  =  56

Example 4 :

Solve for m :

m - 15  =  9

Solution :

Here 15 is subtracted from m.

So, we have to use the inverse operation of subtraction to solve for b.

Inverse operation of subtraction is addition.

m - 15  =  9

m  =  24

Example 5 :

Solve for z :

z + 17  =  23

Solution :

Here 17 is added with z.

So, we have to use the inverse operation of addition to solve for k.

Inverse operation of addition is subtraction.

z + 17  =  23

Subtract 17 from each side.

z  =  6

Example 6 :

Solve for x :

2x + 5  =  23

Solution :

Here 5 is added to 2x.

So, we have to use the inverse operation of addition to solve for 2x.

Inverse operation of addition is subtraction.

2x + 5  =  23

Subtract 5 from each side.

2x  =  18

Here 2 and x are multiplied.

Then, we have to use the inverse operation of multiplication to solve for x.

Inverse operation of multiplication is division.

2x  =  18

Divide each side by 2.

x  =  9

Example 7 :

Solve for p :

2p - 7  =  3

Solution :

Here 7 is subtracted from p.

So, we have to use the inverse operation of subtraction to solve for 2x.

Inverse operation of subtraction is addition.

2p - 7  =  3

2p  =  10

Here 2 and p are multiplied.

Then, we have to use the inverse operation of multiplication to solve for x.

Inverse operation of multiplication is division.

2p  =  10

Divide each side by 2.

p  =  5

Example 8 :

Solve for r :

(r - 6)/2  =  3

Solution :

Here (r - 6) is divided by 2.

So, we have to use the inverse operation of division to solve for (r - 6).

Inverse operation of division is multiplication.

(r - 6)/2  =  3

Multiply each side by 2.

r - 6  =  6

Here 6 is subtracted from r.

Then, we have to use the inverse operation of subtraction to solve for r.

Inverse operation of subtraction is addition.

r - 6  =  6

r  =  12

Example 9 :

Solve for p :

(p/3) - 4  =  0

Solution :

Here 4 is subtracted from (p/3).

So, we have to use the inverse operation of subtraction to solve for (p/3).

Inverse operation of subtraction is addition.

(p/3) - 4  =  0

p/3  =  4

Here p is divided by 3.

Then, we have to use the inverse operation of division to solve for p.

Inverse operation of division is multiplication.

p/3  =  4

Multiply each side by 3.

p  =  12

Example 10 :

Solve for m :

10 - 3m  =  -5

Solution :

10 - 3m  =  -5

10  =  -5 + 3m

15  =  3m

Divide each side by 3.

5  =  m Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 