Question

Seven times the smaller of two consecutive even Integers is the same as - 300 minus 4 times the larger Integer. Find the Integers.

Answer 1

`\Large \textsf{Read below}`

Step-by-step explanation:

`\Large \text{$ \sf 7\:[\:x - 2\:] = -300 - 4x$}`

`\Large \text{$ \sf 7x - 14 = -300 - 4x$}`

`\Large \text{$ \sf 7x + 4x = -300 + 14$}`

`\Large \text{$ \sf 11x = -286$}`

`\Large \text{$ \sf x = -(286)/(11)$}`

`\Large \boxed{\boxed{\text{$ \sf x = -26$}}}`

`\Large \boxed{\boxed{\text{$ \sf (x - 2) = -28$}}}`

Answer 2

The two consecutive even integers that satisfy the given condition are -28 and -26, found by setting up an equation and solving for the unknown smaller integer.

Step-by-step explanation:

The student is asked to find two consecutive even integers such that seven times the smaller integer is the same as -300 minus four times the larger integer. To solve this problem, let's represent the smaller even integer as x, and since even integers are two units apart, the larger even integer will be x+2. The equation based on the problem statement will be:

7x = -300 - 4(x + 2)

Let's solve the equation step-by-step:

1. Expand the right side: 7x = -300 - 4x - 8
2. Combine like terms: 7x + 4x = -300 - 8
3. Simplify: 11x = -308
4. Divide both sides by 11: x = -28

The smaller even integer is -28, and the larger even integer is -26 since it is two units more than the smaller integer.