Adding antifreeze to a car's cooling system can lower the freezing point of the water-based liquids that enable the vehicle to run. (It also raises the boiling point of these liquids.) You added enough antifreeze to lower the freezing point of the liquids to at most (in Celsius). Write the inequality in Fahrenheit.
Watch This
Khan Academy: Multi-Step Inequalities 2
Guidance
Like multi-step equations, multi-step inequalities can involve having variables on both sides, the Distributive Property, and combining like terms. Again, the only difference when solving inequalities is the sign must be flipped when multiplying or dividing by a negative number.
Example A
Is a solution to ?
Solution: Plug in -3 for and see if the inequality is true.
This is a true inequality statement. -3 is a solution.
Example B
Solve and graph the inequality from Example A.
Solution: First, distribute the 2 on the left side of the inequality.
Now, subtract the on the right side to move it to the left side of the inequality. You can also add the 10’s together and solve.
Test a solution,
The graph looks like:
Example C
Solve
Solution: First, combine like terms on the left side. Then, solve for .
Test a solution,
Intro Problem Revisit Recall that the conversion formula for Celsius to Fahrenheit is . The temperature can be equal to or greater than .
So, the temperature can be equal to or higher than .
Guided Practice
1. Is a solution to ?
Solve and graph the following inequalities.
2.
3.
Answers
1. Plug in 12 for and simplify.
This is true because , so 12 is a solution.
2. Distribute the negative sign on the left side and combine like terms.
Test a solution,
3. First, add to both sides and add 21 to both sides.
Test a solution,
Explore More
Determine if the following numbers are solutions to .
Solve and graph the following inequalities.
Solve the following inequalities.
- Solve by adding the term on the right to the left-hand side.
- Solve by subtracting the term on the left to the right-hand side.
- Compare your answers from 12 and 13. What do you notice?
- Challenge Solve . What happens?