# Pre-algebra Practice

Pre algebra introduces students to all the basics of integers and fractions, exponents and square roots, graphs and geometry, which are needed to understand more advanced levels of math. Pre algebra is an important course in high school math since it is repeated in the classes to come and  it finds application in everyday scenarios. Pre algebra is guided by a set of rules and equations and once students understand these, the subject becomes much simpler and not as tough as it is perceived. A structured pre algebra practice module is one of the best ways to learn pre algebra as it takes students through the course step-by-step.

## Pre Algebra Practice Problems

Online pre algebra practice sites have very useful study aids like ready to print sheets which list all the equations and rules in short and succinct points, making them easier to memorize and remember. Students can also find pre algebra practice games and quizzes which facilitate learning by encouraging students to take what they've learned and apply it in practical situations. Algebra can be simple and provided you have a solid understanding of the basics, the rest of your high school algebra classes should be pretty easy to handle. The main idea behind a course like pre algebra is to give students time to get familiar with  using variables, exponents, fractions and associated principles.

## Solved Examples

Question 1: Simplify the Expression:
- 2 - 5$(x + 7)^2$
Solution:
Given - 2 - 5$(x + 7)^2$
Step 1:
Solve for x,

=> - 2 - 5$(x + 7)^2$ = - 2 - 5($x^2$ + $7^2$ + 2 * x * 7)

[ (a + b)2 = a2 + b2 + 2ab ]

= - 2 - 5($x^2$ + 49 + 14x)

= - 2 - 5 * $x^2$ - 5 * 49 - 5 * 14x

= - 2 - 5$x^2$ - 245 - 70x

Step 2:

Combine like terms

=> - 2 - 5$x^2$ - 245 - 70x = - 5$x^2$ - 247 - 70x

or - 5$x^2$ - 70x - 247

=> - 2 - 5$(x + 7)^2$ = - 5$x^2$ - 70x - 247.

Question 2: Imani sold half of her comic books and then bought twenty five more. She now has 52. With how many did she begin?
Solution:
Let Imani begin with x number of comic books

and she sold half of her book = x - $\frac{x}{2}$ = $\frac{x}{2}$, she have.

Step 1:

Given:

Total comic books she have = 52

Number of books she bought = 25

Step 2:

The problem states:

=> $\frac{x}{2}$ + 25 = 52

Subtract 25 from each side

=> $\frac{x}{2}$ + 25 - 25 = 52 - 25

=> $\frac{x}{2}$ = 27

Multiply both side by 2, to isolate the x.

=> $\frac{x}{2}$ * 2 = 27 * 2

=> x = 54

Hence she begin with 54 comic books.

Question 3: Find the value of m. $x^3$ - (x - m)2 = 53, for x = 3.
Solution:
Given, $x^3$ - (x - m)2 = 53

Step 1:

$x^3$ - (x - m)2 = 53

=> $x^3$ - 2x + 2m = 53                   ................(1)

Step 2:

To find the value of m, put x = 3 in equation (1)

=>  $3^3$ - 2 * 3 + 2m = 53

=> 27 - 6 + 2m = 53

=> 21 + 2m = 53

Subtract 21 from both sides

=> 21 + 2m - 21 = 53 - 21

=> 2m = 32

Divide each side by 2

=> $\frac{2m}{2} = \frac{32}{2}$

=> m = 16.

Hence the value of m is 16. answer