How do you solve and graph #5-2x>=27#?

Answer 1

See a solution process below:

First, subtract #color(red)(5)# from each side of the inequality to isolate the #x# term while keeping the inequality balanced:
#5 - color(red)(5) - 2x >= 27 - color(red)(5)#
#0 - 2x >= 22#
#-2x >= 22#
Now, divide each side of the inequality by #color(blue)(-2)# to solve for #x# while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:
#(-2x)/color(blue)(-2) color(red)(<=) 22/color(blue)(-2)#
#(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) -11#
#x <= -11#
To graph this we will draw a vertical line at #-11# on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the left side of the line because the inequality operator also contains a "less than" clause:

graph{x <= -11 [-20, 20, -10, 10]}

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Answer 2

To solve the inequality 5 - 2x ≥ 27, you first subtract 5 from both sides to isolate the term with x. This gives you -2x ≥ 22. Then, divide both sides by -2. Since you're dividing by a negative number, you need to flip the inequality sign. So, x ≤ -11.

To graph this inequality on a number line, you would draw a closed circle at -11 (since it includes -11) and shade everything to the left of -11 to represent all the values of x that satisfy the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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