Write the following sentences using mathematical symbols:
n is greater than -17.
n is less than -10.
w is less than -\dfrac{2}{3}.
y is greater than or equal to -12.
The product of 6 and x is less than or equal to - 42.
The sum of 5 and the product of -4 and x is greater than or equal to 20.
Write the following inequalities in words:
State the largest integer value x can have if x \leq - 2.
State whether the following are solutions of k \leq 15:
Consider the inequality: 12 - y \gt 10.
Find the value of the left-hand side of the inequality when y = 0.
Is y = 0 a solution of 12 - y \gt 10?
State whether the following are solutions of x + 2 \gt 6:
Consider the inequality - 2 x \gt 10. Will the direction of the inequality symbol be reversed when solving this inequality? Explain your answer.
Sally attempted to solve the inequality - 18 - 6 x \gt 30, but has made a mistake. Her working is shown below:
\begin{aligned} &\text{Step } 1: \quad - 18 - 6 x \gt 30\\ &\text{Step } 2: \quad - 6 x \gt 48\\ &\text{Step } 3: \quad x \gt - 8 \end{aligned}What was Sally's mistake?
Solve the following inequalities:
Write the following sentence using mathematical symbols and solve:
"Negative four groups of x is less than three."
Consider the inequality: 6 \left(x + 6\right) \leq 42.
Solve the inequality.
State whether the following are solutions of: 6 \left(x + 6\right) \leq 42.
x = -1
x = 2
x = 0
x = 1
Consider the inequality: 30 + 3 x \gt 30.
Solve the inequality.
State whether the following are solutions of: 30 + 3 x \gt 30.
x = 1
x = 0
x = 3
x = 6
Consider the inequality: 3 \left( 3 x - 4\right) \geq 15.
Solve the inequality.
State whether the following are solutions of: 3 \left( 3 x - 4\right) \geq 15.
x = 0
x = 3
x = 5
x = - 3
Write the following statement as an inequality in terms of T: The temperature T inside a freezer is always below - 15 \degree \text{C}.
Ursula was given \$60 for a birthday present. This present, along with earnings from a Saturday job, are being set aside for a mountain bike. The job pays \$6.50 per hour, and the bike costs \$361.
Write and solve an inequality to find the minimum number of hours that Ursula needs to work to be able to buy the mountain bike, where h represents the number of hours worked.
If Ursula can only work her job for a whole number of hours, find the minimum number of hours she must work to afford her bike.
Ivan wants to save up enough money so that he can buy a new sports equipment set, which costs \$60.00. Ivan has \$21.40 that he has saved from his birthday. In order to make more money, he plans to wash neighbors’ windows for \$4 per window.
Let w be the number of windows that Ivan washes. Write and solve an inequality to find the minimum number of windows he needs to wash in order to afford the equipment.
Find the minimum whole number of windows that Ivan must wash to be able to afford the equipment.
Charlie is saving up to buy a laptop that is selling for \$740. He has \$520 in his bank account and expects a nice sum of money for his birthday next week.
If the amount he is to receive for his birthday is represented by x, write an inequality that models the situation where he is able to afford the laptop.
Would he have enough to buy the laptop if his parents were to give him \$180 for his birthday?
When breeding certain types of fish, it is recommended that the number of female fish is more than triple the number of male fish.
If the number of females is represented by f and the number of males is represented by m, write an inequality that represents the recommended relationship between f and m.
Find a number of female and male fish that would satisfy the recommendation.