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How do you solve #2(x + 6)>= 3x − 2#??

Answer 1

Hazel Anglin

#x<=14#

#2(x+6)>=3x-2#

Work the problem as an equation, keeping in mind the direction of the inequality symbol.

Expand the left side.

#2x+12>=3x-2#

Subtract #2x# from both sides.

#12>=3x-2-2x##=#

#12>=x-2#

Add #2# to both sides.

#12+2>=x##=#

#14>=x#

Switch sides.

#x<=14#

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Answer 2

Jace Anderson

To solve (2(x + 6) \geq 3x - 2), you first distribute the 2 on the left side:

[ 2x + 12 \geq 3x - 2 ]

Then, you can rearrange the equation to isolate the variable (x). To do this, you can subtract (2x) from both sides:

[ 12 \geq x - 2 ]

Next, add 2 to both sides to isolate (x):

[ 14 \geq x ]

So, the solution is (x \leq 14).

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Answer 3

Avery Alexander

To solve the inequality 2(x + 6) ≥ 3x - 2:

Distribute 2 to both terms inside the parentheses: 2x + 12 ≥ 3x - 2
Rearrange the equation to isolate x terms on one side: 2x - 3x ≥ -2 - 12
Combine like terms: -x ≥ -14
Divide both sides by -1 (note that dividing by a negative number reverses the inequality sign): x ≤ 14

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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.

How do you solve #2(x + 6)&gt;= 3x − 2#??

How do you solve #2(x + 6)>= 3x − 2#??