How do you solve the compound equality #2w + 4\geq 2# or #3w + 6\leq 12#?

Question

Write the solution in interval notation.

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Answer 1 · 2018-07-04T03:26:20

#(-oo,oo)#

Let's start with our first inequality

#2w+4>=2#

Let's subtract #4# from both sides to get

#2w>= -2#

Dividing both sides by #2# gives us

#color(blue)(w>= -1)#

Our second inequality is

#3w+6<=12#

Let's subtract #6# from both sides to get

#3w<=6#

Dividing both sides by #3# gives us

#color(purple)(w<=2)#

If we consider our solutions collectively, they include all #x# values.

Because of this, we can interpret this in interval notation as

#(-oo,oo)#

Hope this helps!