Answer:
-5
Explanation:
To find the number, let's break down the problem step by step.
First, let's assign a variable to represent the unknown number. Let's call it "x."
According to the problem, "four less than the sum of a number and 7" can be written as "(x + 7) - 4."
Next, the problem states that this expression is "eight more than twice that number." So, we can write this as "2x + 8."
Now, we can set up an equation based on the information given:
(x + 7) - 4 = 2x + 8
Let's solve this equation to find the value of x.
First, let's simplify the left side of the equation:
x + 7 - 4 = 2x + 8
x + 3 = 2x + 8
Next, let's isolate the variable by subtracting x from both sides:
x - x + 3 = 2x - x + 8
3 = x + 8
To isolate x, we need to get rid of the 8 by subtracting it from both sides:
3 - 8 = x + 8 - 8
-5 = x
Therefore, the number is -5.
To check our answer, let's substitute -5 into the original equation and see if it holds true:
( -5 + 7) - 4 = 2(-5) + 8
2 - 4 = -10 + 8
-2 = -2
The equation holds true, which confirms that the number is indeed -5.