5 times the opposite of a number was 56 less than 2 times the number. What is the number?
To solve this problem, let's assign a variable to represent the number we're looking for. Let's call it "x".
According to the problem, "5 times the opposite of a number" can be written as "5(-x)" or "-5x".
And "56 less than 2 times the number" can be written as "2x - 56".
Based on the given information, we can set up an equation:
-5x = 2x - 56
To solve this equation for x, let's isolate the variable.
First, let's get rid of the 2x on the right side by subtracting 2x from both sides:
-5x - 2x = -56
Combining like terms gives us:
-7x = -56
Now, to isolate x, divide both sides of the equation by -7:
-7x/-7 = -56/-7
Simplifying:
x = 8
Therefore, the number we're looking for is 8.