Question

1. solve for x: 7x + 2 = 30. show your work
2. a rectangles length is x and its width is 4. if the perimeter is 20, write and solve a two - step equation to

find the length.

Explanation:

Step1: Solve for \(x\) in \(7x + 2=30\)

Subtract \(2\) from both sides:
\(7x+2 - 2=30 - 2\)
\(7x = 28\)

Step2: Isolate \(x\)

Divide both sides by \(7\):
\(x=\frac{28}{7}\)

Step3: Solve for the length of the rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is length (\(x\)), \(w\) is width (\(4\)), and \(P = 20\).
First, substitute into the formula: \(20=2(x + 4)\)
Divide both sides by \(2\): \(10=x + 4\)
Subtract \(4\) from both sides: \(x=10 - 4\)

Answer:

For \(7x + 2=30\), \(x = 4\). For the rectangle problem, \(x = 6\) (where \(x\) is the length).