How do you solve and graph #10-x>=3#?

1 Answer
Feb 26, 2017

Answer:

#x<=7#

Explanation:

Using a shortcut tick

To make the #x# positive multiply both sides by (-1). However, in doing this the inequality sign must be turned round the other way.

#color(green)(10-x>=3" "->" "-10+x<=-3)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Why does the sign turn round?")#

Using first principles

#10-x>=3#

Add #x# to both sides

#10+0>=3+x#

Subtract 3 from both sides

#10-3>=x#

this is the same as:

#x<=10-3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Continuing the solution")#

Add 10 to both sides

#color(green)(-10+x<=-3" "->" "0+x<=10-3#

#color(green)(x<=10-3" "->" "x<=7)#

Tony B