Solve out the linear equations, Mathematics

Solve out each of the following equations.

               3( x + 5)= 2 ( -6 - x ) - 2x

Solution

In the given problems we will explained in detail the first problem and the leave most of the explanation out of the following problems.

                               3( x + 5)= 2 ( -6 - x ) - 2x

For this difficulty there are no fractions thus we don't have to worry regarding the first step in the procedure. The next step tells to make simpler both sides.  Thus, we will clear out any parenthesis by multiplying the numbers through & then combine like terms.

                               3(x + 5) = 2 (-6 - x) - 2x

                                  3x+ 15 = -12 - 2x - 2x

                                    3x + 15 = -12 - 4x

The next step is to get all the x's on one side & all the numbers on the other side. Which side the x's go on is up to you and will possibly vary with the problem.  As a rule of thumb usually we will put the variables on the side that will provide a positive coefficient. It is done simply since it is frequently easy to lose track of the minus sign on the coefficient and thus if we ensure it is positive we won't have to worry about it.

Hence, for our case this will mean adding 4x to both of sides and subtracting 15 from both sides.  Notice as well that whereas we will actually put those operations in this time normally we do these operations in our head.

3x+ 15 = -12 - 4 x

3x + 15 -15 + 4x = -12 - 4 x + 4x -15

7 x = -27

 

The next step says to obtain a coefficient of 1 in front of the x.  In this case we can do this by dividing both of sides by a 7.

          7 x/7 = -27/7

            x = - 27 /7

Now, if we've done all of our work accurate x = - 27/ 7 is the solution to the equation.

Then the last & final step is to check the solution.  As pointed out in the procedure outline we have to check the solution in the original equation. It is important, since we may have commit a mistake in the first step and if we did and then checked the answer in the results from that step it might seem to denote that the solution is correct while the reality will be that we don't have the exact answer due to the mistake that we originally made.

The problem of course is that, along with this solution, that verifying might be a little messy.  Let's do it anyway.

 

                24 /7= 24/7               OK

Thus, we did our work properly & the solution to the equation is,

                                x = - 27 /7

Notice that we didn't employ the solution set notation here. For single solutions we will hardly ever do that in this class.  Though, if we had desired to the solution set notation for this problem would be,

                                                             {- 27/7}

Posted Date: 4/6/2013 3:39:39 AM | Location : United States







Related Discussions:- Solve out the linear equations, Assignment Help, Ask Question on Solve out the linear equations, Get Answer, Expert's Help, Solve out the linear equations Discussions

Write discussion on Solve out the linear equations
Your posts are moderated
Related Questions
Two people on bikes are at a distance of  350 meters.  Person A begin riding north at a rate of 5 m/sec and 7 minutes later on Person B begin riding south at 3 m/sec.  Determine th

Symmetry Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set. Defin

Define symmetric, asymmetric and antisymmetric relations.    Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,

in one point of the circle only one tangent can be drawn. prove

Velocity and Acceleration - Three Dimensional Space In this part we need to take a look at the velocity and acceleration of a moving object.    From Calculus I we are famili

I was never really good at mathematics what is the best way? I am reading Math better explained but is there anything else I can do? I want to study advanced topics and get a good

Divides a given line-segment externally in the ratio of 1:2 Construction: i )Draw BX making an actueangle at B. ii) Starting from B, mark 2 equal points on BX as shown in the f

The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale

Ashley's car insurance costs her $115 per month. How much does it cost her per year? Multiply $115 by 12 because there are 12 months in a year; $115 × $12 = $1,380 per year.

Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity.  Through limits at infinity we mean