How do you evaluate the expression 3a+2b for a=1 and b=-2?

Oct 1, 2014

All this question is asking you to do is to solve your given equation when those variables are what they are $\left(a = 1 \mathmr{and} b = - 2\right)$

So that's exactly what we're going to do:

3a + 2b ; a=1, b =-2

$3 \left(1\right) + 2 \left(- 2\right)$ (substitute the values of the variables)

From here on, it's just a matter of condensing down the numbers. Very straightforward, and easy points on tests and quizzes. You can do this in your head if you want, or you can just do it on your calculator (which is probably the best way to go as it's faster and more accurate).

$3 + \left(- 4\right)$ (simplify)

$3 - 4 = - 1$

So here, what we've proven is that in our given equation, if $a = 1$ and $b = - 2$, then it would yield us a product of $- 1$.

Once again, these types of evaluation problems are very straightforward, and are usually always easy points on tests and quizzes if you have an inkling of an idea of what the concept is about. Again, if you have a calculator with all the appropriate functions, that makes it even easier.

Try another: $6 {a}^{2} - b + 8$ with a = 1 and b = 3

$6 {\left(1\right)}^{2} - \left(3\right) + 8$

6 - 3 + 8

= 11

Just as a sidenote here, make sure you're aware of the difference between ${\left(6 x\right)}^{2}$ and $6 {x}^{2}$. The former refers to both the 6 and the $x$ being squared, whereas the latter shows only the $x$ being squared. Just be careful not to mix the two.

Try one more: $\frac{2 c - 5}{3 b + 4}$ with b = 2 and c = 4

$\frac{2 \left(4\right) - 5}{3 \left(2\right) + 4}$

= $\frac{8 - 5}{6 + 4}$

= $\frac{3}{10}$ (or 0.3)

Speaking from experience, when you work with rational (fraction) polynomials on paper, it often tends to take up a bit of space and get messy. Therefore, I'd suggest you tried solving one equation at a time if you have the same issue.

Also, sometimes you may come across values that you don't want to type again in your calculator (like non-recurring decimals). For these, use the store function on your calculator to get maximum accuracy. With TI-84 and 83s, you can save values as letters (X, Y, etc.). Hence, you can just write out your equation using these, and hence significantly reduce the risk of typing the number wrong, while saving yourself some time.

Finally, when substituting in negative values, be SURE to use parentheses to remind you of certain order of operations issues that may affect the problem!