Question

Solve $6x+1=3\left( x-1 \right)+7$ for the value of x.

Answer 1

- Hint: first remove the bracelet by multiplying the constant 3 inside. Now you have variable on both sides. Try to bring the x terms on the left hand side by applying general operations on both sides. And also bring all constants to the right hand side in a similar way. Now, take the coefficient of a in the left hand side and divide with it on both sides. Then you will get the result.

Complete step-by-step solution -

Given expression in the question in terms of x, is written as:
$6x+1=3\left( x-1 \right)+7$
To remove parenthesis, we must multiply 3 inside the bracket:
$\Rightarrow 6x+1=3x-3+7$
The constants on right hand side can be subtracted as:
$\Rightarrow 6x+1=3x+4$
By subtracting 1 on both sides, we get the equation as:
$\Rightarrow 6x+1-1=3x+4-1$
By simplifying the constants on both the sides, we get it as
$\Rightarrow 6x=3x+3$
By subtracting 3x on both sides of equation, we get it as:
$\Rightarrow 6x-3x=3x+3-3x$
By cancelling the common term in right hand side, we get
$\Rightarrow 6x-3x=3$
By taking x common on left hand side, we get it as:
$\Rightarrow x\left( 6-3 \right)=3$
By simplifying left hand side, we get it as:
$\Rightarrow 3x=3$
By dividing with 3 on both sides of equation, we get it as:
$\Rightarrow \dfrac{3x}{3}=\dfrac{3}{3}$
By simplifying the above equation, we get it as:
$\Rightarrow x=1$
Therefore, the value of x satisfying the given equation is 1.

Note: Be careful while solving the parenthesis, generally students keep it as $-1$ itself, don’t forget to multiply 3 if you remove the brackets. Alternately you can keep the variables on the left hand side and constants on the right hand side. You will get the same result anyhow. Whatever operation you apply on the left hand side don’t forget to apply on the right hand side or else you might get the wrong result.