HOW TO SOLVE SIMPLE EQUATIONS

Simple equation is a linear equation in one variable.

Solving simple equation means find the value of the variable. To find the value of the variable, the variable has to isolated.

To isolate the variable in a simple equation, you have to get rid of all the values around the variable using one or more of the following properties of equality.

(i) Addition property of equality.

(ii) Subtraction property of equality.

(iii) Multiplication property of equality.

(iv) Division property of equality.

Example 1 :

Solve for x.

x - 12 = 8

Solution :

x - 12 = 8

Add 12 to both sides.

(x - 12) + 12 = 6 + 12

x - 12 + 12 = 20

x = 20

Example 2 :

Solve for y.

3y + 5 = 26

Solution :

3y + 5 = 26

Subtract 5 from both sides.

(3y + 5) - 5 = 26 - 5

3y + 5 - 5 = 21

3y = 21

Divide both sides by 3.

³ʸ⁄₃ = ²¹⁄₃

y = 7

Example 3 :

Solve for z.

z + 2 = 18 - 3z

Solution :

z + 2 = 18 - 3z

Add 3z to both sides.

(z + 2) + 3z = (18 - 3z) + 3z

z + 2 + 3z = 18 - 3z + 3z

4z + 2 = 18

Subtract 2 from both sides.

4z = 16

Divide both sides by 4.

⁴ᶻ⁄₄ = ¹⁶⁄₄

z = 4

Example 4 :

Solve for a.

9 - a = 3

Solution :

9 - a = 3

Subtract 9 from both sides.

(9 - a) - 9 = 3 - 9

9 - a - 9 = -6

-a = -6

Multiply both sides by -1.

a = 6

Example 5 :

Solve for y.

ʸ⁄₅ = 3

Solution :

ʸ⁄₅ = 3

Multiply both sides by 5.

5(ʸ⁄₅) = 5(3)

y = 15

Example 6 :

Solve for x.

⁽⁵ˣ ⁺ ²⁾⁄₆ = 7

Solution :

⁽⁵ˣ ⁺ ²⁾⁄₆ = 7

Multiply both sides by 6.

6[⁽⁵ˣ ⁺ ²⁾⁄₆] = 6(7)

5x + 2 = 42

Subtract 2 from both sides.

(5x + 2) - 2 = 42 - 2

5x + 2 - 2 = 40

5x = 40

Divide both sides by 5.

⁵ˣ⁄₅ = ⁴⁰⁄₅

x = 8

Example 7 :

Solve for y.

y + ⅔ = ²⁰⁄₃

Solution :

y + ⅔ = ²⁰⁄₃

Multiply both sides by 3 to get rid of the denominator 3 on both sides.

3(y + ) = 3(²⁰⁄₃)

3y + 3() = 20

3y + 2 = 20

Subtract 2 from both sides.

3y = 18

Divide both sides by 3.

³ʸ⁄₃ = ¹⁸⁄₃

y = 6

Example 8 :

Solve for x.

x/0.1 - 1/0.01 + x/0.001 - 1/0.0001 = 0

Solution :

ˣ⁄₀.₁ - ¹⁄₀.₀₁ + ˣ⁄₀.₀₀₁ - ¹⁄₀.₀₀₀₁ = 0

ˣ/⁽¹⁄₁₀₎ - ¹/⁽¹⁄₁₀₀₎ + ˣ/⁽¹⁄₁₀₀₀₎ - ¹/⁽¹⁄₁₀₀₀₀₎ = 0

x(¹⁰⁄₁) - 1(¹⁰⁰⁄₁) + x(¹⁰⁰⁰⁄₁) - 1(¹⁰⁰⁰⁰⁄₁) = 0

10x - 100 + 1000x - 10000 = 0

1010x - 10100 = 0

Add 10100 to both sides.

(1010x - 10100) + 10100 = 0 + 10100

1010x - 10100 + 10100 = 10100

1010x = 10100

Divide both sides by 1010.

¹⁰¹⁰ˣ⁄₁₀₁₀ = ¹⁰¹⁰⁰⁄₁₀₁₀

x = 10

Example 9 :

Four times of a number increased by 7 results 19. What is the number?

Solution :

Let x be the number.

4x + 7 = 19

Subtract 7 from both sides.

(4x + 7) - 7 = 19 - 7

4x + 7 - 7 = 12

4x = 12

Divide both sides by 4.

⁴ˣ⁄₄ = ¹²⁄₄

x = 3

The number is 3.

Example 10 :

3 less than seven times of a number results 53. What is the number?

Solution :

Let x be the number.

7x - 3 = 53

Add 3 to both sides.

(7x - 3) + 3 = 53 + 3

7x + 3 - 3 = 56

7x = 56

Divide both sides by 7.

⁷ˣ⁄₇ = ⁵⁶⁄₇

x = 8

The number is 8.

Example 11 :

Three times Jhon's age 4 years ago is equal to his present age. Find the present age of John.

Solution :

Let x be the present age of John.

It is given that three times Jhon's age 4 years ago is equal to his present age.

3(x - 4) = x

3x - 12 = x

Subtract x from both sides.

(3x - 12) - x = x - x

3x - 12 - x = 0

2x - 12 = 0

Add 12 to both sides.

(2x - 12) + 12 = 0 + 12

2x - 12 + 12 = 12

2x = 12

Divide both sides by 2.

²ˣ⁄₂ = ¹²⁄₂

x = 6

The present age of Joh is 6 years.

Example 12 :

The quotient of a number and 7 is equal to 13. Find the number.

Solution :

Let x be the number.

It is given that the quotient of a number and 7 is equal to 13.

ˣ⁄₇ = 13

Multiply both sides by 7.

7(ˣ⁄₇) = 7(13)

x = 91

The number is 13.

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