Question

Solve: \[3(5x - 7) + 2(9x - 11) = 4(8x - 7) - 111\].

Answer 1

Hint: Equations having variables with power, not more than one is known as linear equations. To find the value of the unknown variable $x$ we shift all the terms involving variables on the left-hand side and bring the constants on the right-hand side. The operations should be performed sequentially as per the BODMAS rules to solve the equation.

Complete answer:
We are given the equation which has an unknown variable $x$ with power one. So, we define it as a linear equation. So to solve this equation we take all the variable terms on the left-hand side and all other terms on the right-hand side. The goal is to keep all the unknown terms involving $x$ on the left-hand side. We apply the BODMAS rule to solve this equation by performing the operations as per the rules.
\[3(5x - 7) + 2(9x - 11) = 4(8x - 7) - 111\]
First, we apply the distributive property and expand the terms.
\[ \Rightarrow 3(5x) - 3(7) + 2(9x) - 2(11) = 4(8x) - 4(7) - 111\]
Then we use the multiplicative property and get the product of the terms.
$ \Rightarrow 15x - 21 + 18x - 22 = 32x - 28 - 111$
We then bring all the variable terms on the left-hand side and all the constants on the right-hand side.
$ \Rightarrow 15x + 18x - 32x = 21 + 22 - 28 - 111$
We perform the addition operation on both sides.
$ \Rightarrow 33x - 32x = 43 - 139$
Lastly, we perform the subtraction operation to get the value of the unknown.
$ \Rightarrow x = - 96$
Hence the required solution to the equation is $x = - 96$ .

Note:
While moving terms from the right-hand side to the left-hand side of the equation the sign of the terms gets changed. This happens similarly for the other side as well. One must take note of that. One must be well aware of the BODMAS rule to perform all the operations sequentially.