Study Practice Algebra Problems

Introduction of Study Practice Algebra Problems:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorial, and number theory, algebra is one of the main branches of pure mathematics. (Source: Wikipedia)

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Study Example Algebra Problems:


Study practice algebra problem 1:

Simplify the equation 5(a -3) + 4b - 7(a -b -3) + 5.

Solution:

5(a -3) + 4b - 7(a -b -3) + 5

Multiply factors.

5a - 15 + 4b -7a + 7b + 21 + 5

Group like terms.

-2a + 11b + 11

Answer:   - 2a + 11b + 11

Study practice algebra problem 2:

To find the 4x - 8y = 9 equation on x-intercept.

Given:

4x - 8y = 9

Solution:

4x - 8y = 9

To find the x intercept of y = 0 and solve for x.

4x - 0 = 9

Solve the value of x.

x = 9 / 4

The x intercept is at the point (9/4, 0).

Answer: x intercept is at the point (9/4, 0).

Study practice algebra problem 3:

16x + 2y = 32.

y + 8 = 16x

Find the x and y value.

Solution:

16x + 2y = 32 (equation 1)

y + 8 = 16x   (equation 2)

Step 1: To choose the equation where the coefficient of the variable is 1.Choose equation 2 to isolate the variable y

y = 16x – 8 (equation 3)

Step 2: From equation 3, we know that y-value is the same as the 16x – 8. We can to substitute the variable y-values in the equation 1 with 16x – 8.

16x + 2 (16x – 8) = 32

Step 3: Remove the brackets by using the distributive property

16x + 32x – 16 = 32

Step 4: To combine the terms

48x – 16 = 32

Step 5: To Isolate the variable of x

48x = 48

x = 48 / 48

x = 1

Step 6: Substitute x = 1 in the equation 3 to get the y-value.

y = 16 (1) – 8

=16 – 8

y = 16 - 8

y = 8

Step 7: To check the answer with the equation (1)

16(1) + 2 (8) = 16+ 16 = 32

Answer: x = 1 and y = 8

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Study Practice Algebra Problems:


Practice Problem 1:

Find the x and y value 12x + 2y = 20, y + 8 = 12x

[Answer: x = 1 and y = 4]

Practice problem 2:

Solve for x and y for the following equations 5x + y = 8, 6x + y = 7

[Answer: x = -1 and y = 13]

Practice Problem 3:

Simplify the equation 7(x -3) + 5y - 3(x -y -3) + 5.

[Answer:   4x + 8y – 7]