Test: Expressions and Formulae - Year 9 MCQ

"Three times a number" translates to 3x, and "increased by five" adds 5 to the expression.

Combine like terms: 2x + 3x = 5x, then 5x − 4.

Perimeter of a rectangle is given by  2(l + w), where l is the length and w is the width.

3x - 7 = 14

Add 7 to both sides of the equation to isolate the term with x:

3x - 7 + 7 = 14 + 7

3x = 21

Divide both sides of the equation by 3 to solve for x:

x = 21/3 = 7

a² - b² = (a - b)(a + b)

Here, 4x² is a perfect square, and 9 is also a perfect square.

We can rewrite the expression as:
4x² - 9 = (2x)² - 3²

Now, applying the difference of squares formula:
(2x)² - 3² = (2x - 3)(2x + 3)

So, the factorized form of 4x² - 9 is:
(2x - 3)(2x + 3)

Solving 2(3x − 4) = 10

Distribute the 2 on the left side:
2 × 3x − 2 × 4 = 10
6x − 8 = 10

Add 8 to both sides to isolate the term with xxx:
6x = 10 + 8
6x = 18

Divide both sides by 6:
x = 18 / 6
x = 3

Multiply both sides of the equation by xxx to get rid of the denominator:
2 = 20x
Divide both sides by 20 to solve for xxx:
x = 2/20
x = 1/10

"Twice a number" is 2x, and "sum with seven" is 2x + 7.

3(2x - 5) + 4(3x + 2)

Distribute the 3 to both terms inside the first parentheses:
3 × 2x - 3 × 5 = 6x - 15

Distribute the 4 to both terms inside the second parentheses:
4 × 3x + 4 × 2 = 12x + 8

Now, combine the like terms:
(6x + 12x) + (-15 + 8) = 18x - 7

Add 16 to both sides:
x² = 16
Take the square root of both sides:
x = ±√16​
Since √16​ = 4, the solutions are:
x = 4
x = −4