An equation is a mathematical sentence with an equal signal. To translate a phrase sentence into an equation, select a variable to characterize one of many unspecified numbers or measures within the sentence. That is known as defining a variable. Then use the variable to jot down equations for the unspecified numbers.

Within the following examples 1-4, translate every sentence into an equation.

Instance 1 :

Twice a quantity elevated by fourteen is an identical to fifty.

Answer :

Let x be the quantity.

Equation :

2x + 14 = 15

Instance 2 :

Half the sum of seven and a quantity is similar because the quantity decreased by two.

Answer :

Let y be the quantity.

Equation :

(1/2)(7 + y) = y – 2

Instance 3 :

The quotient of m and n equals 4 greater than one-third the sum of m and n.

Answer :

Equation :

m/n = (1/3)(m + n) + 4

Instance 4 :

The dice of x plus the sq. of y is the same as fifty two.

Answer :

Equation :

x^{3} + y^{2} = 52

## Consecutive Numbers

Consecutive Integers :

……., -3, -2, -1, 0, 1, 2, 3, …….

n, n + 1, n + 2 are three consecutive integers if n is an integer.

Consecutive Even Integers :

……., -6, -4, -2, 0, 2, 4, 6, …….

n, n + 2, n + 4 are three consecutive integers if n is a good integer.

Consecutive Odd Integers :

……., -5, -3, -1, 0, 1, 3, 5, …….

n, n + 2, n + 4 are three consecutive integers if n is an odd integer.

Within the following examples 5-6, write an equation to characterize the given relationship between integers.

Instance 1 :

The sum of 4 consecutive integers is -54,

Answer :

Let x be the primary integer.

Then, the remaining three integers are

x + 1, x + 2 and x + 3

Equation :

x + (x + 1) + (x + 2) + (x + 3) = -54

Instance 2 :

The product of three consecutive odd integers is 693.

Answer :

Let y be the primary integer.

Then, the remaining two integers are

y + 2 and y + 4

Equation :

y(y + 2)(y + 4) = 693

Instance 3 :

8 lower than the sum of two consecutive integers is the same as 55.

Answer :

Let x be the primary integer.

Then, the second integer is x + 1.

Equation :

x + (x + 1) – 8 = 55

Instance 4 :

5 greater than the product of two consecutive integers is the same as 25.

Answer :

Let y be the primary integer.

Then, the second integer is y + 1.

Equation :

y(y + 1) + 5 = 25

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