The model below can be used to find the quotient of one over two divided by one over six. What is the quotient? A number line from 0 to 1 that is divided into sixths is drawn. Each tick mark is labeled. A tick mark to show the fraction one over two is also shown and labeled. The space between 0 and the first tick mark is circled.
6
3
7/8
6/7

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infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions