#### When solving an inequality how do can you tell if a solution has no solution?

An example of this comes from my homework itself, 4(x+1) = 2x + 4. What steps do I take so I can determine if equations have no solutions whatsoever?

Anonymous

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**How to** find **the** positive integer **solutions to** [math]\frac{**x**}{y+z}+ \frac ...

**The** first thing **to do** when **you**'re looking at **any equation is to** try **and** place it in ....
**for any** particular **solution we** find, **we** just **need to check that** it doesn't **make** ...

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Simplex algorithm - Wikipedia

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) **is**
a popular algorithm **for** linear programming. **The** name of **the** algorithm **is derived**
from **the** concept of a simplex **and** was suggested **by** T. S. Motzkin. Simplices **are**
**not** actually used in **the** method, but **one** interpretation of it **is** .... It **can** also be
shown **that**, **if** an extreme point **is not a** maximum point of **the** ...

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EE364a **Homework 4 solutions**

plain in detail **the** relation between **the** optimal **solution** of each problem **and the**
... in **the** variables **x** ∈ Rn, t ∈ R. **To see the** equivalence, assume **x is** fixed in
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**solving** a ... This **is not a** convex optimization problem, since **the** objective **is not**
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EE364a **Homework** 3 **solutions**

**Solution**. **To** show **that** W **is** quasiconcave **we** show **that the** sets {x | W(x) ≥ α}
**are** convex **for** ... which holds **for any** differentiable convex function, applied **to** g(t)
= t2/**2**. ... **Solution**. **The** feasible set **is** shown in **the** figure. **x1** x2. (1,0). (**2**/5,1/5). (0,
1) ... right, **we see that** Qj = Qk. Thus **the** mapping from **the** index i **to the** index s **is**
.

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R lab **2 solution**

(**Solutions**). **To see** a review of **how to** start R, look at **the** beginning of Lab1 ... **1**.
Probability **that** a normal random variable **with** mean 22 **and** variance 25.

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Support Vector Machines

a decision boundary (this **is the** line given **by the equation** θT **x** = 0, **and is** also
called ... point B lies in-between these two cases, **and** more broadly, **we see that**
**if** a point **is** ... **x** + b). Note **that if** y(i) = **1**, **then for the** functional margin **to** be large (
i.e., **for** .... algorithm **for solving the** above optimization problem **that will** typically
**do**.

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Lecture 5 **1** Linear Programming

Jan 18, 2011 **...** **and so no** feasible **solution has** cost higher than **2**. 3. , **so the solution x1** := 1. 3. ,
x2 := 1. 3 **is** optimal. As **we will see** in **the** next lecture, ... **and** TSP **are** such **that**,
**for** a given input, there **is** only a finite number of possible ... **The** set of feasible
**solutions to** (1) **is the** set of points which satisfy all four **inequalities**,.

For more information, see Lecture 5 **1** Linear Programming

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EE363 **homework 4 solutions**

Now **we can use the** formulas **for the** MMSE estimator in **the** linear ... **do not** help
in estimating **x and we** cannot improve **the** a priori covariance of **x**. **2**. Estimator
error variance **and** correlation coefficient. Suppose (**x**, y) ∈ R2 **is** Gaussian, ... y
**are** almost uncorrelated, i.e., |ρ| **is** small, **we** find **that** η ≈ **1**, which mean **that the**.

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Triviality (mathematics) - Wikipedia

In mathematics, **the** adjective trivial **is** frequently used **for** objects **that have** a very
simple structure. **The** noun triviality usually refers **to** a simple technical aspect of
some proof or ... Trivial **can** also be used **to** describe **solutions to** an **equation that**
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**If** **x** + y = **2** \text{ **and** } **x**^**2** + y^**2** = **2**, what **is the** value of ...

I'm **not** sure what math **you**'re in. Anyway, **the** straightforward way **is to solve for** y
in **the** first **equation**, **and** plug ... Middle **and** High School Math **Homework**
Question ... Well **one** way **to solve** it **would** be by squaring **the** first **equation and**
...... R: **So you can see that the** final **solution is x** = **1 and** y = 1 **so** x.y=1, because 1
*1=1.

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Cubic **Formula** -- from Wolfram MathWorld

**The** cubic **formula is the** closed-form **solution for** a cubic **equation**, i.e., **the** ...
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**If you take the** reciprocal in an **inequality**, **would** it change **the**

Jul 4, 2016 **...** I also remark **that** inverting a sum **is not the** same as inverting **the** ..... **You can**
**take** reciprocals using only multiplication **and** division. In algebra, there **are** rules
**for** what **you can do to** an **equation** or **inequality to make** sure it stays true. ... **you**
**can turn** it into its reciprocal **equation by taking the** following **steps**:.

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asymptotics - Big Theta Proof on polynomial function - Computer ...

Sep 16, 2013 **...** **So your** approach **is** valid, **and** it's possible **that the solution** from **your** class **is** ...
**is** error-prone, though: it's easy **for you to make** a mistake along **the** way. It **is** ...
Start from what **you know is** true, **and then** derive **the** implications of **that**, ending
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For more information, see asymptotics - Big Theta Proof on polynomial function - Computer ...

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mathematics - **1 2** 3 **4** 5 6 7 8 9 = 100 - Puzzling Stack Exchange

Apr 14, 2015 **...** **If you** allow exponents, **you can get** away **with** just two: **1** .... I **can** confirm there **is**
**no** better **solution** than Andrew Smith's **if we use the** operators +-*/. ... There **are**
215 possibilities total **and the** number of **solutions for the** number of ... I **know that**
technically **I do not have** a shorter **solution**, but I applied **the** ...

For more information, see mathematics - **1 2** 3 **4** 5 6 7 8 9 = 100 - Puzzling Stack Exchange

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linear programming - How **the** dual LP solves **the** primal LP ...

**If you use the** simplex method or some variant of it, **you are** actually
simultaneously **solving the** primal **and** dual. **That is**, from an optimal simplex
tableau **you can** read off both an optimal **solution** ... From an optimal **solution** of
either primal or dual, complementary slackness .... **See my** other answer **for** a (
hopefully) correct **one**.

For more information, see linear programming - How **the** dual LP solves **the** primal LP ...

Mahesh Godavarti

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Essentially, when there is no solution, it means that there is no value of x that satisfies the equation or the inequality.

Let's start with the simplest one.

x = x + 1 (does this equation have any solutions?. Obviously not, because there is no way a number is equal to itself plus one)

How can we show this? Subtract x from both sides, then we get

0 = 1 (which cannot be true)

Therefore, x = x + 1 has no solutions.

Let's take an inequality

x > x (does this inequality have any solutions? Obviously not, because a number cannot be greater than itself!)

Subtract x from both sides we get

0 > 0 (which is not true, since 0 is not greater than 0. Therefore, x > x has no solutions).

The way to show whether an equation or inequality has no solutions is to manipulate the equation or inequality till we end up with a statement that is false.

-------------------

Let's take the homework question.

4(x + 1) = 2x + 4

4x + 4 = 2x + 4

Subtract 4 from both sides

4x = 2x

Subtract 2x from both sides

2x = 0

Divide both sides by 2

x = 0.

Therefore, this equation has a solution. That is the statement becomes true when x = 0.

-----------------------

Let's take the second example.

9 - 5x + 2 = 4 - 5x

11 - 5x = 4 - 5x

Subtract 4 from both sides

7 - 5x = -5x

Add 5x to both sides

7 = 0

(This is not a true statement! There is no value of x, that will make the left hand side of the equation equal to the right hand side. Therefore, there are no solutions.)