three times the smaller of two consecutive even integers is the same as -146 minus 4 times the the larger integer.
3 x = -146 - 4(x + 2)
7 x = - 154
Let's solve this step-by-step:
1. Let's denote the smaller even integer as "x".
2. Since we are considering two consecutive even integers, the larger one will be "x + 2" (as "x + 2" will always be the next even number after "x").
3. We are given that three times the smaller integer is the same as -146 minus 4 times the larger integer. We can write this as the following equation:
3x = -146 - 4(x + 2)
4. Now, let's solve the equation:
3x = -146 - 4x - 8
3x + 4x = - 146 - 8
7x = -154
5. Divide both sides of the equation by 7:
x = -154 / 7
6. Simplify the fraction or use a calculator to find the decimal value:
x ≈ -22
7. Since the smaller integer cannot be a decimal, let's round it down to -22.
8. The larger integer is "x + 2":
-22 + 2 = -20
Therefore, the two consecutive even integers are -22 and -20.
To solve this problem, let's proceed step by step.
Let's assume that the smaller even integer is represented by "x", and the larger even integer is represented by "x + 2" since the two integers are consecutive even integers.
According to the problem, three times the smaller integer is equal to -146 minus 4 times the larger integer. We can write this equation as:
3x = -146 - 4(x + 2)
Let's solve this equation to find the value of "x."
First, simplify the equation by distributing -4 to (x + 2):
3x = -146 - 4x - 8
Next, combine like terms:
3x + 4x = -146 - 8
7x = -154
Now, isolate "x" by dividing both sides of the equation by 7:
x = -154 / 7
Calculating this value gives us:
x ≈ -22
So, the smaller even integer is approximately -22.
To find the larger even integer, we can substitute the value we found for "x" into our assumption:
x + 2 = -22 + 2
x + 2 = -20
Therefore, the larger even integer is -20.
Hence, the solution to the problem is that the smaller even integer is approximately -22, and the larger even integer is -20.