Question

three times the sum of a number and -5 equals -6 times the sum of the number and -2. Find the number.

Answer 1

"Three times the sum of a number and -5" - let the number be x.

"times" indicates multiplication, and "sum" indicates addition. Ignore the "times" part first; that leaves you with "the sum of a number and -5," which is x + (-5) or x - 5. Now include the multiplication bit, and you get 3(x - 5). This will be equal to "-6 times the sum of the number and -2." Similarly, the sum of the two numbers will be multiplied by the first number, -6. You get -6(x - 2). Now you have:

3(x - 5) = -6(x - 2)

Solve. Apply the Distributive Property: a(b + c) = ab + ac.

3(x - 5) = -6(x - 2)

3x - 15 = -6x + 12

Add 15 to both sides to get rid of the constant on the left side of the equation.

3x - 15 = -6x + 12

3x - 15 + 15 = -6x + 12 + 15

3x = -6x + 27

Add 6x to both sides to get rid of the variable term on the right side of the equation.

3x = -6x + 27

3x + 6x = -6x + 27 + 6x

9x = 27

Divide both sides by 9 to isolate x.

9x = 27

9x/9 = 27/9

x = 3

Answer:

The number is 3.

Answer 2

3(x-5)=-6(x-2)

3x-15=-6x+12

9x-15=12

9x=27

x=3