Question

directions: translate each expression, then write the expression in factored form.

1. \the sum of four times a number and twenty - four\
2. \the difference between nine times a number and seventy - two\
3. \ten times a number, subtracted from eighteen\
4. \thirty more than the product of six and a number\

Explanation:

Problem 16 (First "16"): "the sum of four times a number and twenty - four"

Step 1: Define the variable

Let the number be \( x \). Four times a number is \( 4x \).

Step 2: Translate the sum

The sum of \( 4x \) and 24 is \( 4x + 24 \).

Step 3: Factor the expression

We can factor out the greatest common factor, which is 4. So, \( 4x+24 = 4(x + 6) \).

Step 1: Define the variable

Let the number be \( x \). Nine times a number is \( 9x \).

Step 2: Translate the difference

The difference between \( 9x \) and 72 is \( 9x-72 \).

Step 3: Factor the expression

We can factor out the greatest common factor, which is 9. So, \( 9x - 72=9(x - 8) \).

Step 1: Define the variable

Let the number be \( x \). Ten times a number is \( 10x \).

Step 2: Translate the subtraction

"Ten times a number, subtracted from eighteen" means \( 18-10x \).

Step 3: Factor the expression

We can factor out the greatest common factor, which is 2. So, \( 18 - 10x=2(9 - 5x) \).

Answer:

Translated: \( 4x + 24 \); Factored: \( 4(x + 6) \)

Problem 17: "the difference between nine times a number and seventy - two"