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Solve the inequality below. Write your solution in interval notation. If there is no solution, write "no solution"

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Solve the inequality below. Write your solution in interval notation. If there is-example-1

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Answer:
\boldsymbol{(-\infty, 3]}

There's a square bracket for the endpoint "3".

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Work Shown

First we isolate x.


3 - (4x+1) \ge 5x-25\\\\3 - 4x-1 \ge 5x-25\\\\-4x+2 \ge 5x-25\\\\-4x-5x \ge -25-2\\\\-9x \ge -27\\\\x \le (-27)/(-9)\\\\x \le 3

The inequality sign flips when dividing both sides by a negative number.

The inequality
x \le 3 can be thought of as
-\infty < x \le 3

That would then condense to the interval notation
\boldsymbol{(-\infty, 3]}

We use a square bracket for the "3" to include that endpoint.

Either infinity will always get a curved parenthesis.

User Wrager
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