Question

How do you solve \[4[x-(3-2x)]+5=3(x+11)\]?

Answer 1

Hint: In this question, first we will expand the terms in the parenthesis on the left and right side of the equation by multiplying each term within the parenthesis by the term outside the parentheses. After that, we will arrange the equation and simplify the equation. After that, we will get the value of x by simplifying the equation.

Complete step by step answer:
Let us solve this question.
The given equation that we have to solve is
\[4[x-(3-2x)]+5=3(x+11)\]
Let us now expand the terms in the parenthesis on the both sides of the equation.
\[\Rightarrow 4(x)-4(3-2x)+5=3(x)+3(11)\]
Expand the terms again which are in the parenthesis, we get
\[\Rightarrow 4(x)-4(3)-4(-2x)+5=3(x)+3(11)\]
We can write the above equation as
\[\Rightarrow4x-12+8x+5=3x+33\]
As we know that there are only linear terms in the above equation. So, we will convert them into a standard form of linear equation that is x=C, where x is variable and C is constant.
Now, we will convert the above equation in standard form.
Now, we will take all the terms of x to the left side of the equation and all constant terms to the right side of the equation.
\[\Rightarrow 4x+(12-12)+8x+(5-5)-3x=(3x-3x)+33+12-5\]
 After solving, we get the above equation as
\[\Rightarrow 4x+8x-3x=33+12-5\]
The above equation also can be written as
\[\Rightarrow 9x=40\]
Now, we divide 40 by 9 to get x.
\[\Rightarrow x=\dfrac{40}{9}\]
After dividing 40 by 9, we get
x=4.444

Note: We can solve questions by a different method that is addition subtraction property.
After expanding the terms within the parentheses and simplifying the equation, we get
\[4x-12+8x+5=3x+33\]
We have to make all the terms of x on the left side of the equation and all the constants on the right side of the equation. So, after using the addition subtraction property, the above equation can also be written as
\[\Rightarrow4x+8x-3x=33+12-5\]
\[\Rightarrow 9x=40\]
\[\Rightarrow x=\dfrac{40}{9}\]
Hence, the value of x is 4.444