Answered

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".

Verified Answer :

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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

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

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"

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