How do you solve and graph the compound inequality #3>=4r  5>= 1# ?
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To solve the compound inequality ( 3 \geq 4r  5 \geq 1 ), first, solve each inequality separately and then intersect their solutions.

Solve ( 3 \geq 4r  5 ): ( 3 + 5 \geq 4r ) ( 8 \geq 4r ) ( 2 \geq r )

Solve ( 4r  5 \geq 1 ): ( 4r \geq 1 + 5 ) ( 4r \geq 4 ) ( r \geq 1 )
Intersecting the solutions, we find the common solution to both inequalities is ( 1 \geq r \geq 2 ).
To graph the solution on a number line:
 Mark a point at ( r = 1 ) and shade to the left.
 Mark a point at ( r = 2 ) and shade to the right.
 Draw brackets on both ends to indicate that the inequality includes ( 1 ) and ( 2 ).
This results in a shaded region between ( r = 1 ) and ( r = 2 ) on the number line.
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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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