You are planning a trip to Spain in the summer. In the U.S., we use Fahrenheit to measure the temperature, but in Europe, they use Celsius. To get yourself used to Celsius, you find the equation
Solving an algebraic equation for a variable can be tricky, but it can also be very useful. This technique can be used to go back and forth between two different units of measurement. To solve for, to isolate, a variable within an equation, you must undo the operations that are in the equation.
Solution: To solve for
Now we need to get
When undoing multiplication, you must divide everything in the equation by 3.
A few things to note:
- To undo an operation within an equation, do the opposite.
- Perform the opposite operations in the reverse order of the Order of Operations.
- Combine all like terms on the same side of the equals sign before doing #1.
Given the equation
Solution: This example combines what was learned in the last section with what we did in the previous example. First, isolate
Now, we have a fraction multiplied by
Even though we know that a 9 can be pulled out of the 18 and the 9 in the above equation, it is not a necessary step in solving for
The area of a triangle is
Solution: First solve the equation for
Now, plug in what we know to find
This process is helpful when solving for any variable in any equation or formula. Some formulas you may need to know for this text are listed below.
|Area of a Triangle||
|Area of a Rectangle||
|Area of a Circle||
|Area of a Trapezoid||
|Perimeter of a Rectangle||
|Circumference of a Circle||
Intro Problem Revisit First, let's substitute in
As you can see, a good estimator for the conversion is to double the degrees, when in Celsius, and then add 32. Needless to say, it is going to be quite hot in Spain and you should pack summer clothes.
2. If the temperature is
1. First add
2. You can solve this problem two different ways: First, plug in 41 for
Now, plug in 41 for
Solve the following equations or formulas for the indicated variable.
6x−3y=9; solve for y.
4c+9d=16; solve for c.
5f−6g=14; solve for f.
13x+5y=1; solve for x.
45m+23n=24; solve for m.
45m+23n=24; solve for n.
P=2l+2w; solve for w.
F=95C+32; solve for C.
Find the value of
For questions 13-15, use the formulas in the chart above to answer the following questions.
- If the temperature is
86∘F, what is it in Celsius?
- If the area of a circle is
36π cm2, what is the radius?
- The area of a trapezoid is
72 ft2, the height is 8 ft and b1is 6, what is the length of the other base?
For questions 16-17, use the equation for the surface area of a cylinder,
- Solve the equation for
hif the surface area is 120π cm2and the radius is 6 cm.
Challenge The formula for the volume of a sphere is
V=43πr3. Solve the equation for r, the radius.