How do you solve and write the following in interval notation: # [(2x − 6)/(x+1)] ≤1#?

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Answer 1 · 2017-12-02T21:28:19

#x\rightarrow [-\infty,7]#

We can isolate for #x# by algebraically manipulating the inequality:

#\frac{2x-6}{x+1}\leq 1#

Multiply both sides by #x+1#:

#\implies 2x-6\leq 1(x+1)#

Subtract #x# from both sides:

#\implies x-6\leq 1#

Add #6# to both sides:

#\implies x\leq 7#

This means #x# can take on a value of any that #7# or less, which can be expressed in interval notation as:

#[-\infty,7]#