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How do you solve and graph the compound inequality #7>-5x+6# or #10<= -5x+3# ?

Answer 1

Avery Alexander

#7 > 5x + 6 -> 5x < 1 -> x < 1/5#

#10 <= - 5x + 3 -> 5x <= -7 -> x <= -7/5#

==============|-7/5----------|0-----|1/5---------------

Answer #x <= -7/5#

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Answer 2

Abigail Allen

To solve and graph the compound inequality (7 > -5x + 6) or (10 \leq -5x + 3):

Solve each inequality separately: For (7 > -5x + 6): [7 > -5x + 6] [1 > -5x] [-\frac{1}{5} < x]

For (10 \leq -5x + 3): [10 \leq -5x + 3] [7 \leq -5x] [-\frac{7}{5} \leq x]
Combine the solutions by considering the "or" condition: The compound inequality solution is (-\frac{7}{5} \leq x < -\frac{1}{5}).
Graph the solution on a number line: Place an open circle at (-\frac{7}{5}) and shade to the left. Place a closed circle at (-\frac{1}{5}) and shade to the right.

The graph represents the solution to the compound inequality.

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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 and graph the compound inequality #7&gt;-5x+6# or #10&lt;= -5x+3# ?

How do you solve and graph the compound inequality #7>-5x+6# or #10<= -5x+3# ?