Question

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

Shown in picture.

Answer 1

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.