Question

Write the expressions "Four times the difference of a number and 7 is 32", "One third of a number is 12 less than the number itself", "Ten increased by the quotient of a number and 2 is -15", and "One less than the product of a number and 3 is 5 more than the number itself".

Answer 1

Answer:

1) $4(x-7)=32$

2) $\frac{1}{3}x=x-12$

3) $10+\frac{x}{2}=-15$

4) $(3x)-1=5+x$

Step-by-step explanation:

Given : Expressions in words.

To find : The expressions value?

Solution :

Let x be the number,

According to question,

1) "Four times the difference of a number and 7 is 32"

$\Rightarrow 4(x-7)=32$

2) "One third of a number is 12 less than the number itself"

$\Rightarrow \frac{1}{3}x=x-12$

3) "Ten increased by the quotient of a number and 2 is -15"

$\Rightarrow 10+\frac{x}{2}=-15$

4) "One less than the product of a number and 3 is 5 more than the number itself"

$\Rightarrow (3x)-1=5+x$

Answer 2

Part 1) "Four times the difference of a number and $7$ is $32$"

Let

x--------> the number

we know that

the expressions is equal to

$4(x-7)=32$

therefore

the answer part 1) is

$4(x-7)=32$

Part 2) "One third of a number is $12$ less than the number itself"

Let

x--------> the number

we know that

the expressions is equal to

$\frac{1}{3} x=(x-12 )$

therefore

the answer part 2) is

$\frac{1}{3} x=(x-12 )$

Part 3) "Ten increased by the quotient of a number and $2$ is $-15$"

Let

x---------> the number

we know that

the expressions is equal to

$10+ (\frac{x}{2} )= -15$

therefore

the answer Part 3) is

$10+ (\frac{x}{2} )= -15$

Part 4) "One less than the product of a number and $3$ is $5$ more than the number itself"

Let

x---------> the number

we know that

the expressions is equal to

$(3x)-1=5+x$

therefore

the answer Part 4) is

$(3x)-1=5+x$