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

### Solved Examples

**Question 1:**Simplify the Expression:

- 2 - 5$(x + 7)^2$

**Solution:**

Given - 2 - 5$(x + 7)^2$

Solve for x,

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

[ (a + b)

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

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

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

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.

**Step 1:**Solve for x,

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

[ (a + b)

^{2}= a^{2}+ b^{2}+ 2ab ]= - 2 - 5($x^2$ + 49 + 14x)

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

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

Step 2: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.

Given:

Total comic books she have = 52

Number of books she bought = 25

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.

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

Step 1:Step 1:

Given:

Total comic books she have = 52

Number of books she bought = 25

Step 2: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

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

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

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.

Step 1:Step 1:

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

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

Step 2: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**