Equations
Equations
An equation includes an equal sign (e.g., 3x + 2xy = 17) and states that two expressions are equal. Solving an equation means finding the value(s) of the variable that makes the equation true. To do this, isolate the variable on one side of the equation. This can be done by following the same simple steps.
- Distribute to get rid of parentheses.
- Use the least common denominator to get rid of fractions.
- Add/subtract like terms on either side.
- Add/subtract so that constants appear on only one side of the equation.
- Multiply/divide to isolate the variable.
2(2x − 8) = x + 7 | |
|---|---|
4x − 16 = x + 7 | Distribute. |
4x − 16 − x = x + 7 − x 3x − 16 = −7 | Subtract x to isolate the variable on one side. |
3x − 16 + 16 = −7 y + 16 3x = 9 | Add 16 to both sides. |
\(\frac{3x}{3} = \frac{9}{3}\) x= 3 | Divide both sides by 3. |
You can perform any operation on an equation as long as you do it to both sides of the equation.
Mathematic expressions and equations can be used to model real-life situations. Often these situations are presented as word problems that can be translated into mathematical terms and solved. No matter the problem, this process can be completed using the same steps:
- Read the problem carefully and identify the value to be solved for.
- Identify the known and unknown quantities in the problem. Assign variables to represent the unknowns.
- Translate the problem to an equation.
- Solve the equation.
- Check the solution: Is the question answered? Does it make sense?
The table below gives some common phrases and their translation into mathematical terms.
Translating Word Problems | ||
|---|---|---|
Words | Math Translation | Example |
equals, is, will be, yields, the same as | = | a is the same as b a = b |
add, increase, added to, sum, combined, more than | + | 2 more than x x + 2 |
minus, decreased, less than, subtracted, take away, difference between | − | 3 less than n n − 3 |
multiplied by, times, product of | × | the product of a and b a × b |
divided by, per, out of | ÷ | x divided by y x ÷ y |