# B1.05: Section 4

Evaluate variable expressions when given the value of each variable, using the correct order of operations. Recall these rules about order of operations. Do them in this order.

- All operations inside symbols of grouping (parentheses) from the inside out.
- All operations of exponents or roots.
- All multiplications and divisions, in order from left to right.
- All additions and subtractions, in order from left to right.

### Example 1

Evaluate [latex]y=6+2x[/latex] when [latex]x=7[/latex].Answer:

Solution: [latex]\begin{align}&y=6+2x\\&y=6+2\cdot(\,\,\,)\\&y=6+2\cdot(7)\\&y=6+2\cdot7\\&y=6+14\\&y=20\\\end{align}[/latex] | Notice that the 7 here is in parentheses, but it is not an OPERATION in parentheses, so there is no need to think about that first rule in the order of operations. |

### Example 2

Evaluate [latex]y=u{{x}^{4}}[/latex] when [latex]x=2\,\,\,and\,\,\,u=9[/latex].Answer: [latex-display]\begin{align}&y=u{{x}^{4}}\\&y=(\,\,)\cdot{{(\,\,)}^{4}}\\&y=(\,9)\cdot{{(\,2)}^{4}}\\&y=9\cdot{{2}^{4}}\\&y=9\cdot16\\&y=144\\\end{align}[/latex-display] Discussion: Later in the course, some students have trouble remembering not to do the multiplication of 9 times 2 here first. Many of our formulas will include exponents such as this, so it is important to learn this rule well.

### Checking your work

When evaluating expressions, the only clear method to check your work is to simply re-work it. That’s not completely satisfactory because if you have a mistake in understanding, you’re likely to make it both times. However, in this course, most of the times when we will evaluate an expression, it is in the context of a larger problem for which there is a good method of checking available.## Licenses & Attributions

### CC licensed content, Shared previously

- Mathematics for Modeling.
**Authored by:**Mary Parker and Hunter Ellinger.**License:**CC BY: Attribution.