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How do you solve the graph: 1<3x-2≤10?

Answer 1

Abigail Allen

#1 < x <= 4#
as a line graph:

Given an inequality, you can

add the same amount to both sides
divide both sides by any amount greater than zero without effecting the validity or orientation of the inequality

#1 < 3x-2 <=10#

can be split into two inequalities

#1 < 3x-2# #color(white)("XXX")rarr 3 < 3x# #color(white)("XXX")rarr 1 < x#

and

#3x-2 <= 10# #color(white)("XXX")rarr 3x <= 12# #color(white)("XXX")rarr x <= 4#

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Answer 2

Ethan Adkins

To solve the inequality 1 < 3x - 2 ≤ 10, follow these steps:

Add 2 to all parts of the inequality: 1 + 2 < 3x - 2 + 2 ≤ 10 + 2 This simplifies to: 3 < 3x ≤ 12
Divide all parts of the inequality by 3: 3/3 < 3x/3 ≤ 12/3 This simplifies to: 1 < x ≤ 4

So, the solution to the inequality is 1 < x ≤ 4.

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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 the graph: 1&lt;3x-2≤10?

How do you solve the graph: 1<3x-2≤10?