Question

Five less than the quotient of a number and three is -7

Answer 1

Answer:

The unknown number is -6

Step-by-step explanation:

Let's start by writing the sentence in mathematical terms:

Since we don't know what that "number" is, we replace it with the letter "$x$". Then, the quotient of that unknown number and three can now be written as: $\frac{x}{3}$

"Five less than the quotient of a number by three", can then be written as the difference (where we are subtracting 5 from that quotient): $\frac{x}{3} -5$

The last part of the sentence tells us that the expression we just wrote in mathematical form "is -7." This in mathematical terms indicates "equals -7."

Therefore, we now have a mathematical equation (there is an equal sign in the expression) and we try to solve for the unknown number "$x$" in it:

$\frac{x}{3} -5=7$

We do such by isolating the x on one side of the equal sign. This process involves: first add 5 on both sides of the equation, and second:multiply both sides of the equation by 3 to get rid of the denominator under the unknown:

$\frac{x}{3} -5=-7\\\frac{x}{3} -5 +5 = -7 +5\\\frac{x}{3} =-2\\\frac{x}{3} * 3 = -2 *3\\x=-6$