Question

Solve the inequality. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters.3x+2 \geq 7x-1AnswerAnswer,AnswerAnswer

Answer 1

(-inf, 0.75]

Step-by-step explanation:

In order to solve the inequality

`3x+2\ge7x-1`

we first subtract 2 from both sides to get:

`3x\ge7x-1-2`

next, subtracting 7x from both sides gives

`3x-7x\ge-1-2`
`-4x\ge-3`

Now we divide both sides by - 4. Remember that whenever we divide by a negative number, the equality changes sign. Therefore, the above becomes

`-(4x)/(-4)\le-(3)/(-4)`
`x\le(3)/(4)`

since in decimal form 3/4 = 0.75, the above becomes

`\boxed{x\le0.75}`

Hence, all values of x less than or equal to 0.75 satisfy the inequality.

Now how do we write x ≤ in the interval notation?

The answer is

`(-\infty,0.75\rbrack`

which means all values of from ( and not including) -infinity to 0.75 (included) satisfy the inequality.