Question

1. the perimeter of a rectangle is 48 inches. if the length is 4 inches more than twice the width, find the dimensions.
2. the sum of two consecutive integers add to 12 is equal to -11 find both numbers.

Explanation:

Step1: Let the first integer be \(x\)

The second consecutive integer is \(x + 1\)

Step2: Set up the equation

\(x+(x + 1)=-11\)

Step3: Simplify the left - hand side

\(2x+1=-11\)

Step4: Solve for \(x\)

Subtract \(1\) from both sides: \(2x=-11 - 1=-12\)
Divide both sides by \(2\): \(x=\frac{-12}{2}=-6\)

Step5: Find the second integer

The second integer is \(x + 1=-6+1=-5\)

Answer:

The two consecutive integers are \(-6\) and \(-5\)