Question
What /g the 1 Tuqulion 4Y equation Ixt 4 of the 1cunaing "anempoint and pupuluicuiaTucin?Mumdlis JuiUI UnonessidmUzan1 11
What /g the 1 Tuqulion 4Y equation Ixt 4 of the 1 cunaing "anempoint and pupuluicuia Tucin? Mumdlis JuiUI Unonessidm Uzan 1 1 1
Answers
Solve each equation. $$\frac{y-1}{y+4}=\frac{y+1}{y-2}$$
We're being asked to solve the given equation for why? Well, to do this, we can first add one to both sides of our equation. So we do. Left with 14 fly is equal to negative one. Now, what I'm gonna do is multiply both sides of our equation by four. Well, four times 1/4. Why is simply just why and negative one times four is equal to negative for. And now we've solved our equation and we found the solution toe are given. Equation is negative for
We're being asked to solve the given absolute value equation, The absolute value of four -Y is equal to one. Well remember absolutely. When you take the absolute value of number, you're trying to find its distance from zero on the number line. So in this case because our absolute value is equal to one, we're trying to find what values that why could be Such that when we take the absolute value of this expression we get one meaning that the value inside our absolute value could simply be one. So for minus why could equal to one. However -1 is also one Union away from zero. Therefore four -Y could also be equal to -1. So now we're just gonna solve both equations. So to solve the first equation we subtract four from both sides, 1 -4 is -3. So that's all for why we divide by negative one and negative three divided by one is positive three. And it's the same steps to solve the second equation, we begin by subtracting four so we have negative Y is equal to negative five, and then we divide by negative one and negative five, divided by negative one, is positive five. So now we have our two solutions three and 5.
They were going to solve the equation. Why squared? Plus 1/4 is equal to minus wine. In order to do this, we're going to multiply everything by four and bring everything to you the same side. So you get four y squared plus for why plus one is equal to zero. Now we are, since the coefficient of y squared is like the one we will take the coefficient of y squared and multiply it by a constant, which is one which is four. And then we'll also write our term in our coefficient of why we're looking for two numbers am be such that eight times beers for but a plus B is also for now the factors of 414 and then two times two and clearly due to do plus two Z before So we factories. This is two plus two. This tells us we write this as four y squared plus two y plus two y plus one is equal to zero. Then we can factor out to wife from our first term, giving those two y plus one with, in fact, route one from our second time, giving us to place two y plus one. So when we factor out to wife plus one from our first him well, from better terms, we're left with a surplus of two y plus one. In fact, this is just two y plus one all squared Andi. This is equal to zero. Therefore, ah, there is a solution when determining bracket is equal to zero. So two y plus one is equal to zero. Telling us to y is equal to minus one, telling us that why is equal to minus 1/2. There's only one solution, and it's a double root of this equation, I think.
Right here. We need to multiply both sides by four. And that gives me. He's canceling out and I get negative eight on this side. So why minus one equals negative eight. Now add one to both sides. I get why this equal seem negative seven.