What is the combined length of all the buttons longer than 1 inch

 inches

Step-by-step explanation:

The "x" represents the number of buttons.

There are 2 sizes longer than 1 inch:

in  and   in

There are NO 1  1/8 inch buttons

THere are two 1  1/4 inch buttons

Hence the combined length would be:

inches

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