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

Question

contestada

Respuesta :

GurjotY187117 GurjotY187117 · Answer 1 · 2022-10-30T00:22:08+02:00

Answer:

(-inf, 0.75]

Explanation:

In order to solve the inequality

[tex]3x+2\ge7x-1[/tex]

we first subtract 2 from both sides to get:

[tex]3x\ge7x-1-2[/tex]

next, subtracting 7x from both sides gives

[tex]3x-7x\ge-1-2[/tex][tex]-4x\ge-3[/tex]

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

[tex]-\frac{4x}{-4}\le-\frac{3}{-4}[/tex][tex]x\le\frac{3}{4}[/tex]

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

[tex]\boxed{x\le0.75}[/tex]

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

[tex](-\infty,0.75\rbrack[/tex]

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