Question

1. what is the solution of the equation below? 0.1(20x + 100)=3x + 10 (a) x = 0 (b) x = 1/2 (c) x=-10 (d) no solution 7. a rectangular football field has a width that is two more than three times the length. which of the following equations could be used to find the length if the perimeter of the field is 400? (a) 2(3x + 2)+2x = 400 (b) 2(3x + 2)+2x = 400 (c) 3x + 2 = 400 (d) 3x + 2 + x = 400 8. the length of a rectangle is nine more than twice the width. write a simplified expression that could be used to find the perimeter of the rectangle.

Explanation:

Step1: Solve the equation \(0.1(20x + 100)=3x + 10\)

First, distribute the \(0.1\) on the left - hand side: \(0.1\times20x+0.1\times100 = 3x + 10\), which simplifies to \(2x+10 = 3x + 10\).

Step2: Isolate the variable \(x\)

Subtract \(2x\) from both sides: \(2x+10-2x=3x + 10-2x\), getting \(10=x + 10\). Then subtract \(10\) from both sides: \(10-10=x+10 - 10\), so \(x = 0\).

Answer:

A. \(x = 0\)