Question

How do you solve $14+5x=3\left( -x+3 \right)-11$ ?

Answer 1

Hint: We are asked to find the solution of $14+5x=3\left( -x+3 \right)-11$
Firstly, we learn what the solution of the equation means, then we will learn what linear equation is in 1 variable term. We use a hit and trial method to find the value of “$x$”. In this method we put the value of ”$x$“ one by one by hitting arbitrary values and looking for needed values. Once we work with a hit and trial method we will try another method where we apply algebra. We subtract, add or multiply terms to get to our final term and get our required solution. We will also learn that doing the questions using algebraic tool make them easy

Complete step-by-step solution:
We are given that we have $14+5x=3\left( -x+3 \right)-11$we are asked to find the value of”$x$“, or we are asked how we will be able to solve this expression.
Solution of any problem is that value which when put into the given problem then equation is satisfied
Now we learn about the equation on one variable. One variable simply represents the equation that has one variable (say x, y, or z) and another one constant.
For Example:
$x+2=4,2x,2y$ Etc.
Our equation $14+5x=3\left( -x+3 \right)-11$ also has just one variable”$x$“
We have to find the value of ”$x$“ which will satisfy our given equation.
Firstly we try by the method of hit and trial. In which we will put a different value of ”$x$“ and take which one fits the solution correctly.
Let $x=0$
We put $x=0$ in $14+5x=3\left( x+3 \right)-11$
We get
$14+5\times 0=3\left( -0+3 \right)-11$
$14=9-11$
$14=-2$
Not true
Hence $x=0$ is not the solution
Let
$x=1$
We put $x=1$ in $14+5x=3\left( -x+3 \right)-11$
We get
$\Rightarrow $ $14+5\left( 1 \right)=3\left( -1+3 \right)-11$
$\Rightarrow $ $19=6-11$
$\Rightarrow $ $19=-5$
Not true
So $x=1$ is also not solution
We can see that the difference between terms increased.
So it means we are on wrong way
So we move along the negative side.
Let $x=-2$
We put $x=-2$ in $14+5x=3\left( -x-13 \right)-11$
We get
$\Rightarrow $ $14+5\left( -2 \right)=3\left[ -\left( -2 \right)+3 \right]-11$
$\Rightarrow $ $14-10=15-11$
$\Rightarrow $ $4=4$
This is true
So $x=-2$ is true solution
Remember that it is necessary to check that we are on the right track or not, i.e., we don’t check if this process will get messy.
We will try the way, in which we use Algebraic tools to solve problems.
As we have
$14+5x=3(-x+3)-11$
We open braced
$14+5x=-3x+9-11$
Simplify we get
$14+5x=-3x-2$
We added $3x$ on both and subtract 14 on both sides
$14+5x+3x-14=-3x+3x-2-14$
Simplifying we get
$8x=-16$
Divide both side by 8, we get
$\dfrac{8x}{8}=\dfrac{-16}{8}$
$x=-2$
So solution is $x=-2$

Note: Remember that, we cannot add the variable to the constant. Usual mistakes like this where one adds constants with variables usually happen.
For example: $3x+6=9x$, here one added ‘6’ with 3 of x made it 9x, this is wrong, we cannot add constant and variable at once. Only the same variables are added to each other.
When we add the variable the only constant part is added or subtracted variable remains same that is $2x+2x=4x$ error like doing it $2x+2x=4{{x}^{2}}$ may happen so be careful there
Remember when we divide positive term by negative value the solution we get is a negative term this may happen that we skip - sign
We need to choose the best techniques as per the question if the question is defined using variable only time so hit and trials would be ok but if the equation has more time variable then we go for the arithmetic tool