Question

The quotient of a number and -5 increased by one is at most 7. please need hellp

Answer 1

n ≥ -40

Explanation:

`n-\text{a number}\\\\\text{the quotient of a number and - 5}\to n:(-5)=-(n)/(5)\\\\\text{the quotient of a number and -5 increased by one}\to-(n)/(5)-1\\\\\text{the quotient of a number and -5 increased by one is at most 7}:\\\\-(n)/(5)-1\leq7\qquad\text{add 1 to both sides}\\\\-(n)/(5)-1+1\leq7+1\\\\-(n)/(5)\leq8\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup\cdot\left(-(n)/(5\!\!\!\!\diagup)\right)\leq(5)(8)\\\\-n\leq40\qquad\text{change the signs}\\\\n\geq-40`