Question

How do you solve $2x+\dfrac{3}{4}\left( 4x+16 \right)=7$?

Answer 1

Hint: In this question, we are given an equation in terms of x and we need to solve this equation to find the value of x which will satisfy the equation. For this we will perform certain operations i.e. addition, subtraction, multiplication, division on both sides of the equation such that we are left with the variable x on the left side of the equation. The constant term will give us the required value of x which satisfies the equation.

Complete step by step answer:
Here we are given the equation in terms of x as $2x+\dfrac{3}{4}\left( 4x+16 \right)=7$.
We need to find the value of x which satisfies this equation. For this let us perform certain operations, (addition, subtraction, multiplication, division) on both sides of the equation such that we are left with variable x on the left side of the equation and a constant on the right side of the equation. We should get the form as x = c where c is the constant and required value of x.
Our equation is $2x+\dfrac{3}{4}\left( 4x+16 \right)=7$.
First of all let us open the bracket and simplify the left side of the equation. The equation becomes $2x+\dfrac{3}{4}\times 4x+\dfrac{3}{4}\times 16=7$.
Cancelling 4 by 4 in the second term and dividing 16 by 4 to get 4 in the third term of the left side of the equation we get $2x+3x+3\times 4=7$.
Solving we get $2x+3x+12=7$.
As we can see 2x and 3x are like terms and can be added to get a single term with variable x. So adding 2x with 3x we get $5x+12=7$.
As we can see, 12 is a constant that is not required on the left side of the equation so to remove it let us subtract 12 from both sides of the equation we get $5x+12-12=7-12\Rightarrow 5x=7-12$.
Solving the constant on the right side we see that 12-7 = 5 but the negative sign is with 12 which is greater. Therefore, we will have 7-12 = -5. Hence our equation reduces to $5x=-5$.
The equation is not in the form as x = c as there is a coefficient of x. So let us remove it.
Dividing both sides of the equation by 5 we get $\dfrac{5x}{5}=\dfrac{-5}{5}$.
As we know 5 divided by 5 gives the answer 1 so we have x = -1.
Hence the required value of x is -1 which will satisfy the given equation.

Note:
Students should always take care of the signs while solving the equation. Make sure to use proper operation as required. Students can also check their answers by following way,
Putting x = -1 in the original equation $2x+\dfrac{3}{4}\left( 4x+16 \right)=7$ we get,
$2\left( -1 \right)+\dfrac{3}{4}\left( 4\left( -1 \right)+16 \right)=7$.
Simplifying we get $-2+\dfrac{3}{4}\left( -4+16 \right)=7$.
Solving the bracket first we get $-2+\dfrac{3}{4}\times 12=7$.
12 divided by 4 gives 3 so we get $-2+3\times 3=7$.
$3\times 3$ gives us 9 so we get $-2+9=7\Rightarrow 7=7$.
Left hand side is equal to the right hand side of the equation so the found value of x is the correct answer.