Question

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

Answer 1

Answer:

n ≥ -40

Step-by-step explanation:

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