## How to Evaluate One Variable?

So, in mathematics, we refer to a variable as an unknown entity or something that can have no fixed value. For example, let us consider the case of natural numbers. In a set of natural numbers, $$n$$ can be defined as anything between $$1$$ and infinity. So, $$n$$ belongs to the set of Integers ($$1, \ 2, \ 3, \ 4$$, ………). Therefore, in this case we can consider $$n$$ as a variable because it has some definite value, but that value is not fixed. It completely depends on the numerical problem that what value of a particular variable should we use.
Moreover, in an expression, a variable can have coefficients and exponential powers. For example, $$4x^3$$ is a variable with an exponent power of $$3$$ and a co-efficient value of $$4$$. So, variables can be found in just pure form (for example $$x^3$$) and even in mixed form (like $$5x^2$$).
Also, in an expression, we can simplify the variable terms by grouping them into like and unlike terms. We should perform all mathematical operations separately to these like and unlike term groups.

### How to Evaluate One Variable?

To evaluate a single variable, we must follow the given steps:

• If possible, first simplify the variable expression.
• Next, just substitute the value of the variable in the equation.

Example Questions

• Substitute for $$x \ = \ 6$$ in $$x^2 \ + \ 6x \ + \ 7 \ = \ 6^2 \ + \ 6(6) \ + \ 7 \ = \ 36 \ + \ 36 \ + \ 7 \ = \ 79$$.
• Substitute for $$x \ = \ 3$$ in $$x \ + \ 7 \ = \ 3 \ + \ 7 \ = \ 10$$.
• Substitute for $$x \ = \ 5$$ in $$x^2 \ + \ 5x \ + \ 12 \ = \ 5^2 \ + \ 5(5) \ + \ 12 \ = \ 25 \ + \ 25 \ + \ 12 \ = \ 62$$.
• Substitute for $$x \ = \ 3$$ in $$x^3 \ + \ 4x^2 \ + \ 7 \ = \ 3^3 \ + \ 4(3^2) \ + \ 7 \ = \ 27 \ + \ 36 \ + \ 7 \ = \ 70$$.
• Substitute for $$x \ = \ 2$$ in $$x^3 \ - \ 7x^2 \ + \ 14 \ = \ 2^3 \ - \ 7(2^2) \ + \ 14 \ = \ 8 \ - \ 28 \ + \ 14 \ = \ -6$$.
• Substitute for $$x \ = \ 1$$ in $$x^3 \ - \ 2x^2 \ + \ 7x \ - \ 6 \ =$$
$$1^3 \ - \ 2(1^2) \ + \ 7(1) \ - 6 \ = \ 1 \ - \ 2 \ + \ 7 \ - \ 6 \ = \ 0$$.

### Exercises for Evaluating One Variable

1) $$x \ = \ 6, \$$$$x \ - \ 4 =$$

2) $$x \ = \ 8, \$$$$5x \ - \ 4 =$$

3) $$x \ = \ 21, \$$$$x \ - \ 3 =$$

4) $$x \ = \ -5, \$$$$8x \ + \ 5 =$$

5) $$x \ = \ -12, \$$$$8x \ + \ 6 =$$

6) $$x \ = \ 3, \$$$$3x \ + \ 8 =$$

7) $$x \ = \ 10, \$$$$6x \ + \ 6 =$$

8) $$x \ = \ -7, \$$$$\frac{28}{x} \ + \ 5 =$$

9) $$x \ = \ -14, \$$$$\frac{56}{x} \ + \ 8 =$$

10) $$x \ = \ 9, \$$$$\frac{18}{x} \ + \ 6 =$$

1) $$x \ = \ 6, \$$$$x \ - \ 4 =$$$$\ \color{red}{6 \ - \ 4 \ = \ 2}$$
2) $$x \ = \ 8, \$$$$5x \ - \ 4 =$$$$\ \color{red}{5 \ \times \ 8 \ - \ 4 \ = \ 36}$$
3) $$x \ = \ 21, \$$$$x \ - \ 3 =$$$$\ \color{red}{21 \ - \ 3 \ = \ 18}$$
4) $$x \ = \ -5, \$$$$8x \ + \ 5 =$$$$\ \color{red}{8 \ \times \ (-5) \ + \ 5 \ = \ -35}$$
5) $$x \ = \ -12, \$$$$8x \ + \ 6 =$$$$\ \color{red}{8 \ \times \ (-12) \ + \ 6 \ = \ -90}$$
6) $$x \ = \ 3, \$$$$3x \ + \ 8 =$$$$\ \color{red}{3 \ \times \ 3 \ + \ 8 \ = \ 17}$$
7) $$x \ = \ 10, \$$$$6x \ + \ 6 =$$$$\ \color{red}{6 \ \times \ 10 \ + \ 6 \ = \ 66}$$
8) $$x \ = \ -7, \$$$$\frac{28}{x} \ + \ 5 =$$$$\ \color{red}{28 \ \div \ (-7) \ + \ 5 \ = \ 1}$$
9) $$x \ = \ -14, \$$$$\frac{56}{x} \ + \ 8 =$$$$\ \color{red}{56 \ \div \ (-14) \ + \ 8 \ = \ 4}$$
10) $$x \ = \ 9, \$$$$\frac{18}{x} \ + \ 6 =$$$$\ \color{red}{18 \ \div \ (9) \ + \ 6 \ = \ 8}$$

## Evaluating One Variable Practice Quiz

### Prepare for the PSAT / NMSQT Math Test in 7 Days

$17.99$12.99

### Prepare for the AFOQT Math Test in 7 Days

$25.99$14.99

### TABE 11 & 12 Math Study Guide

$20.99$15.99

### HSPT Math Study Guide 2020 - 2021

$20.99$15.99