TRANSLATING PHRASE INTO EQUATIONS AND INEQUALITIES

To translate phrase into equation or inequality, we have to be aware of the following terms.

+ Sum, more, plus x Times, multiplied, product

- Difference, less, subtracted / Divided by, quotient

Write the sentence as an equation or an inequality. Let x represent  the number.

Problem 1 :

The sum of 20 and a number is 30.

Solution :

Let x be the number.

As per the question,

x + 20 = 30

Hence, the equation is x + 20 = 30.

Problem 2 :

A number increased by 10 is greater than or equal to 44.

Solution :

Let x be the number.

As per the question,

x + 10 ≥ 44

Hence, the inequality is x + 10 ≥ 44.

Problem 3 :

18 decreased by a number is 6.

Solution :

Let x be the number.

As per the question,

x - 18 = 6

Hence, the equation is x - 18 = 6.

Problem 4 :

35 is less than the difference of 21 and a number.

Solution :

Let x be the number.

As per the question,

35 < x - 21

Hence, the inequality is 35 < x - 21.

Problem 5 :

The product of 13 and a number is greater than 60.

Solution :

Let x be the number.

As per the question,

13x > 60

Hence, the inequality is 13x > 60.

Problem 6 :

7 times a number is 56.

Solution :

Let x be the number.

As per the question,

7x = 56

Hence, the equation is 7x = 56.

Problem 7 :

A number divided by 22 is less than 3.

Solution :

As per the question,

x/22 < 3

Hence, the inequality is x/22 < 3.

Problem 8 :

The quotient of 35 and a number is 7.

Solution :

As per the question,

35/x = 7

Hence, the equation is 35/x = 7.

Problem 9 :

A number x divided by 9 is less than 17.

Solution :

As per the question,

x/9 < 17

Hence, the inequality is x/9 < 17.

Problem 10 :

The product of 10 and a number x is 50.

Solution :

As per the question,

10x = 50

Hence, the equation is 10x = 50.

Problem 11 :

A number y plus 10 is greater than or equal to 57.

Solution :

As per the question,

y+10 ≥ 57

Hence, the inequality is y+10 ≥ 57.

Problem 12 :

A number y minus 6 is 15.

Solution :

As per the question,

y - 6 = 15

Hence, the equation is y - 6 = 15.