I'm currently confused on telling whether an absolute value equation has a solution or doesn't. for example, -5|x + 1| = 10 has no solution, and if you actually did it, the x would be -3, and 1. meanwhile 2|x − 6| + 14 = 38 has a solution of x = −6, x = 18 and it has a i'm so confused.

Afactory adds 3 red drops and 2 blue drops of coloring to white paint to make each pint of purple paint. the factory will make 50 gallons of the purple paint.how many drops of red and blue coloring will the factory need in the 50 gallon batch of purple paint.

Atheater wants to build movable steps that they can use to go on and off the stage. they want the steps to have enough space inside so they can also be used to store props. how much space is inside the steps?

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.