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Solve the inequality 2x - 5 <= -x +12 - 3x + 6. Give your answer as an interval.

 
 Sep 11, 2021
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Explanation: First, add 5 to each side of the inequality to isolate the absolute value function while keeping the inequality balanced: | 2 x + 1 | − 5 + 5 < 0 + 5 | 2 x + 1 | − 0 < 5 | 2 x + 1 | < 5.

The absolute value function takes any term and transforms it to its non-negative form.

Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

− 5 < 2 x + 1 < 5.

Next, subtract 1 from each segment of the system of inequalities to isolate the x term while keeping the system balanced:

− 5 − 1 < 2 x + 1 − 1 < 5 − 1 − 6 < 2 x + 0 < 4 − 6 < 2 x < 4

Now, divide each segment of the system by 2 to solve for x while keeping the system balanced:

− 6 2 < 2 x 2 < 4 2 − 3 < 2 x 2 < 2 − 3 < x < 2 Or x > − 3 and x < 2

Or, in interval notation: ( − 3 , 2 )

 
 Sep 11, 2021

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