"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.
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