Answer :
a. negative nine decreased by 3 times a number
negative nine is -9.
Let a certain number be ' p '
3 times a certain number is 3p.
Hence, we can write this equation as -9 - 3p.
b. the difference between 3 and a number
Let a certain number be ' p '
Hence, we can write this equation as 3 - p.
c. the difference between three times a number and eight
Let a certain number be ' p '
3 times a certain number is 3p.
Hence, we can write this equation as 3p - 8.
d. the difference of 3 times the number x and 12 is -24
3 times a number x is 3x.
Hence, we can write this equation as 3x - 12 = 24.
e. the difference between three times a number and 4 is -19.
Let a certain number be ' p '
3 times a certain number is 3p.
Hence, we can write this equation as 3p - 4 = -19.
f. 2 times the difference between x and 3.
the difference between x and 3 is (x - 3).
2 times (x - 3) is 2(x - 3).
Hence, this equation is 2(x - 3).
g. the quotient of x and 3.
The quotient is obtained after the division of two numbers.
Hence, this equation can be written as x/3.
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The complete question is -
Interpret the following algebraic expressions.
a. negative nine decreased by 3 times a number
b. the difference between 3 and a number
c. the difference between three times a number and eight
d. the difference of 3 times the number x and 12 is -24
e. the difference between three times a number and 4 is -19.
f. 2 times the difference between x and 3.
g. the quotient of x and 3.