TMUA Algebraic Techniques & Manipulation

Question 1

Simplify: 2x + 3x - 5

Accepted Answer

5x - 5

Answer

To simplify the expression, combine the like terms. The terms 2x and 3x are like terms, so adding them together gives 5x. The constant term -5 remains unchanged, resulting in the simplified expression 5x - 5.

Question 2

Solve for x: 3x = 12

Accepted Answer

4

Answer

To solve for x, you need to isolate x on one side of the equation. Divide both sides of the equation 3x = 12 by 3. This yields x = 12 / 3, which simplifies to x = 4.

Question 3

Factor: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

This expression is a difference of squares, which follows the algebraic identity a² - b² = (a - b)(a + b). Here, a = x and b = 3 (since 3² = 9). Therefore, x² - 9 factors into (x - 3)(x + 3).

Question 4

Expand: (x + 2)(x - 2)

Accepted Answer

x² - 4

Answer

This is an example of the difference of squares formula, (a + b)(a - b) = a² - b². Here, a = x and b = 2. So, expanding (x + 2)(x - 2) directly results in x² - 2². This simplifies to x² - 4.

Question 5

What is the solution to the equation x² = 16?

Accepted Answer

x = ±4

Answer

To solve for x, take the square root of both sides of the equation. The square root of 16 is 4, but it's important to remember that both positive and negative values, when squared, will result in a positive number. Therefore, x can be either 4 or -4, denoted as x = ±4.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Algebraic Techniques & Manipulation