Question

How do you solve $3\left( 1-3x \right)=2\left( -4x+7 \right)$ ?

Answer 1

Hint: This is a linear equation in one variable, so one equation is sufficient to solve for the variable. We can bring the variable to one side; it may be LHS or RHS, and the constant values to the other side and then solve for x by dividing both LHS and RHS by coefficient of x.

Complete step by step answer:
The given equation in the question is $3\left( 1-3x \right)=2\left( -4x+7 \right)$
Further solving by multiplying 3 with the term 1 – 3x in LHS and multiplying 4 with term -4x + 7 in RHS , we get
$\Rightarrow 3-9x=-8x+14$
Now we can bring all the x to LHS and all the constant to RHS
Adding 8x to both LHS and RHS we get
$\Rightarrow 3-x=14$
Now adding -3 in LHS and RHS we get
$\Rightarrow -x=11$
Now we can multiply or divide LHS and RHS by -1
$\Rightarrow x=-11$

We can see the value of x is 11.

Note: The equation given in the question was a linear equation in one variable, so one equation is enough to solve it. If there are n unknown variables then minimum n linear equations are required to evaluate all the unknown variables. Sometimes n equations are enough if the delta value of the entire coefficients is 0. If there are n unknown variables and less than n equations then the number of solutions tends to infinity. If there are more than n equations then there may not exist any solution for the system.