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 "[tex]x[/tex]". Then, the quotient of that unknown number and three can now be written as: [tex]\frac{x}{3}[/tex]
"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): [tex]\frac{x}{3} -5[/tex]
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 "[tex]x[/tex]" in it:
[tex]\frac{x}{3} -5=7\\[/tex]
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:
[tex]\frac{x}{3} -5=-7\\\frac{x}{3} -5 +5 = -7 +5\\\frac{x}{3} =-2\\\frac{x}{3} * 3 = -2 *3\\x=-6[/tex]
