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Wize High School Algebra I Textbook (Common Core) > Solving One-Variable Equations

Solving Equations & Formulas

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Solving Equations & Formulas

Equations

Recall: An equation is an algebraic expression that involves an equal sign.

If the question asks you to solve the equation that has one variable, you have to find a number to replace the variable so that the left side of the equation equals the right side of the equation. To do this, we want to get the variable to appear on one side by itself.

Example (questions you may be asked)
Solve the equation 2x−1=92x-1=9

Wize Tip
The golden rules for solving an equation are:
  1. Whatever you do to the left side of the equation, you must do the same thing to the right side -- the equation must stay "balanced" at the = sign.
  2. To "get rid of" or "move" something to the other side of the equal sign, you must do the opposite operation
  3. The opposite of +3+3 is −3-3
  4. The opposite of −3-3 is +3+3
  5. The opposite of ×3\times3 (which will look like 3x3x) is ÷3\div3
  6. The opposite of ÷3\div3 (which will look like x3\frac{x}{3}) is ×3\times3
  7. The opposite of ...2{...}^2 is ...\sqrt{...}

Formulas

A formula is just an equation, but there will be more than one variable.

The question can ask you to solve for a specific variable in the formula, in this case, pretend the other variables are just numbers. Sometimes the question might give you numbers to replace the other variables with.

Examples (questions you may be asked)
1. Solve for bb in the formula A=b×h2A=\dfrac{b\times h}{2}

2. Solve for rr in the formula A=πr2A=\pi r^2, where A=3A=3

Practice: Solving Equations

Solve the following equation for xx.

3(2x−16)=−2(2−2x)3\left(2x-\dfrac{1}{6}\right)=-2\left(2-2x\right)

Practice: Solving Equations

Solve the following equations for ww.

w−2(4−w)=−12(5w−17)w-2(4-w)=-\dfrac{1}{2}(5w-17)

Practice: Solving Equations

Temperature is commonly measured in degrees Celcius °C\degree C or degrees Fahrenheit °F\degree F, here's the formula to convert between the two:
(C×95)+32=F\left(C\times\dfrac{9}{5}\right)+32=F
a) Write an equation that represents 41°F41\degree F.
b) Solve the equation in a) to determine the temperature in degrees CC.
c) Rearrange the equation (C×95)+32=F\left(C\times\dfrac{9}{5}\right)+32=F to isolate for CC (solve for CC in terms of FF).

Practice: Solving Equations

The perimeter PP of a rectangle is given by the formula P=2(L+W)P=2\left(L+W\right), where LL is the length and WW is the width.

a) Create an equation where the perimeter is 5050 meters and the length is 66 meters.

b) Solve the equation in part a) to determine the width of the corresponding rectangle.

c) Isolate for LL in the equation P=2(L+W)P=2\left(L+W\right). (Solve for LL).

Practice: Solving Equations

A circular pool has an area of 15 m215\text{~m}^2, determine the radius of this pool.

Check out the hints if you need a refresher on the area of a circle.