How do you solve the inequality #abs(3x5)<=4# and write your answer in interval notation?
See a solution process below:
The absolute value function takes any term and transforms it to its nonnegative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
Or
Or, in interval notation:
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To solve the inequality ( 3x  5 \leq 4 ) and express the solution in interval notation:

Solve for the two cases of the absolute value:
 ( 3x  5 \leq 4 ) and ( 3x  5 \geq 4 )

Solve each inequality separately:
 For ( 3x  5 \leq 4 ), add 5 to both sides and divide by 3: ( 3x \leq 9 ), so ( x \leq 3 )
 For ( 3x  5 \geq 4 ), add 5 to both sides and divide by 3: ( 3x \geq 1 ), so ( x \geq \frac{1}{3} )

Combine the solutions:
 The solution is ( \frac{1}{3} \leq x \leq 3 )

Express the solution in interval notation:
 ( \left[ \frac{1}{3}, 3 \right] )
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To solve the inequality (3x  5 \leq 4) and write the answer in interval notation, follow these steps:
 Split the absolute value inequality into two separate inequalities: (3x  5 \leq 4) and (3x  5 \geq 4).
 Solve each inequality separately for (x).
 Combine the solutions into one interval.
Solving the first inequality: [3x  5 \leq 4] [3x \leq 9] [x \leq \frac{9}{3}] [x \leq 3]
Solving the second inequality: [3x  5 \geq 4] [3x \geq 1] [x \geq \frac{1}{3}]
Combining the solutions: The solution set for the inequality (3x  5 \leq 4) is the interval ([ \frac{1}{3}, 3 ]).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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