when-the-equation-2-frac3bfrac5b2-is-solved-for-b-the-solutions-are-1-and-3-explain-why-the-number-l

Question

When the equation $2-\frac{3}{b}=\frac{5}{b+2}$ is solved for $b$ , the solutions are $-1$ and $3 .$ Explain why the number line must be separated into five segments by the numbers $-2,-1,0,$ and 3 in
order to check the solution set of the inequality $2-\frac{3}{b}>\frac{5}{b+2}$

Dale Sanford · Accepted Answer

we&#x27;re told that if the greater than symbol here is replaced with an equal sign Ah, the solution to this equation would be b equals negative one and three. However, if we were to write this inequality out on a number line, we would have that the number line should be split at negative one and three as well as negative two and zero. Well, this is because when b equals negative one or three, then we have that these two sides are equal and we only care about the places where this side is greater than this side. If the left side is equal to the right side than it&#x27;s not greater than so, we don&#x27;t care about it in our interval. Additionally, if you plug in B equals two, then this term right here becomes we&#x27;re sorry. Negative to not positive. We get five over negative two plus two, which is 5/0, which doesn&#x27;t exist. So we&#x27;ll have to break the number line there. And this term, if you plug in B equals zero becomes 3/0, which doesn&#x27;t exist. So the number line will be split up at negative one and three because those will set the two sides equal and it will be split up at negative two and zero because those will make this inequality not exist.

Martha Richards · Answer

so are given this equation here and asked to solve the inequality and then put it onto a number line. So the first thing we&#x27;re gonna d&#x27;oh Issa track three. So I have the absolute value of B is less than or equal to two. So then, because we&#x27;re taking the absolute here, we know that Ah, positive B is greater than our ear is less than or equal to two. And we also know that the negative B is less than or equal to two. So just solve for B. We divide both sides by a negative one or multiply. Either way, that works best for you. And when we do that, we gotta flip the sign. And so that means that he&#x27;s gonna be greater than a negative too, but greater than or equal to. So here. This will start this at zero. And so this is negative too. So we have a solid line here, and it&#x27;s greater than but it&#x27;s got to be less than a positive, too. So that means that this is graft by going between negative, too, because it&#x27;s gonna be greater than a negative too, and a less than or equal thio a positive too

Brandon Fox · Answer

Let&#x27;s start by distributing the three into the prince. Sees three times a is three a in three times. A two is a plus six. Now let&#x27;s combine three a in minus five. A three minus five is negative. Two. So right as a minus two A. To get the A&#x27;s together, I&#x27;m going to go ahead and, um, actually add to a double size. What that will happen is the minus 28 and the two able cancel. I&#x27;ll just have six. And on the other side I&#x27;ll have to and then I&#x27;ll add negative one plus two cause a zai can add those together and I get a plus a plus one a not a gay by itself also tracked to Apple Science. So a is less than or equal to, and I get six months to wishes for

Ankit Gupta · Answer

we have to solve the equation, which is more X minus one. Listen X minus three. So we get X minus one less than X minus three and x minus one. Weirder than minus X minus three. No, but still living this Regan minus one less than ministry. This is not possible. From this aggression, we get two X greater than for. So you get the video to this. Iniquity signifies that directness. This reality signifies that old excluded them. Do Bill. Hell, this property that more X minus two is less than no X minus three. This implies that distance off X I do is less than from three.

Ali Soave · Answer

we&#x27;ll start to solve the equation or the involving by adding five total sites. These cancel out. We&#x27;re left with B, and greater then and negative two plus five is three. If it&#x27;s easier for you to understand when you flip it around, we have biggest less than three. That means we&#x27;re gonna be shaving to the left on a number line. So let&#x27;s draw our number. One will put a few numbers here. 12 and three Open open circle at three, since it does not have an equal to science and then we&#x27;ll shade to the left.

Will Cadelina · Answer

to solve this inequality. Three is less than or equal to 1/2 plus a start by rewriting three as six halves. This will make it easier to be subtracted by 1/2 of the next step. Now we conserve track 1/2 from both sides to get rid of the 1/2 you should end up with this life. Halves is less than or equal to a. This is also equal to two, and 1/2 is less than a. This makes it easier to see where will be on the graph. Now let&#x27;s graph it, since 2.5 is less than or equal to a, this means a is more than or equal to 2.5. Since a can equal 2.5, we&#x27;re gonna do a hollow bubble at 2.5. This represents the smallest quantity that a could be. Since they can only be more than 2.5 or equal to it, we&#x27;re gonna draw Ray going to the right. This is where all the larger values that they can be. This is a graph of your solution, and the solution is five halves is less than or equal to a or 2.5 is less than or equal to a

Problem

What is the solution set of $\frac{|x|}{x}<0 ?$ J…

Problem 1 Easy Difficulty

When the equation $2-\frac{3}{b}=\frac{5}{b+2}$ is solved for $b$ , the solutions are $-1$ and $3 .$ Explain why the number line must be separated into five segments by the numbers $-2,-1,0,$ and 3 in
order to check the solution set of the inequality $2-\frac{3}{b}>\frac{5}{b+2}$

Answer

Because $-1$ and 3 are solutions of the corresponding equation and $-2$ and 0 are roots of the denominators (and thus values at which the equation is undefined).

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Algebra Educators

Catherine R.

Heather Z.

Alayna H.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Alayna H.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Because $-1$ and 3 are solutions of the corresponding equation and $-2$ and 0 are roots of the denominators (and thus values at which the equation is undefined).

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Alayna H.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Alayna H.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry