HOW TO SOLVE SIMPLE EQUATIONS

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 + ⅔) = 3(²⁰⁄₃)

3y + 3(⅔) = 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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