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# How do you solve $6(5 - 8v) + 12 = - 54?$

Last updated date: 13th Jun 2024
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Hint: First of all take the given expression, open the bracket in the equation multiplying the term outside bracket inside the bracket and then move all the terms on one side of the equation, then will find the resultant required value for “v”.

Complete step-by-step solution:
Take the given expression: $6(5 - 8v) + 12 = - 54$
Open the bracket multiplying the term outside the bracket with the terms inside the bracket.
$\Rightarrow 30 - 48v + 12 = - 54$
Move the term with the variable on the right hand side of the equation and constant on the left hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Negative terms become positive and vice-versa.
$\Rightarrow 30 + 12 + 54 = 48v$
Simplify the above like terms on the left hand side of the equation.
$\Rightarrow 96 = 48v$
The above equation can be re-written as-
$\Rightarrow 48v = 96$
The term multiplicative on one side if moved to the opposite side then it goes to the denominator.
$\Rightarrow v = \dfrac{{96}}{{48}}$
Find factor for the term on the numerator on the right hand side of the equation.
$\Rightarrow v = \dfrac{{48 \times 2}}{{48}}$
Common factors from the numerator and the denominator cancel each other. Therefore remove from the numerator and the denominator.
$\Rightarrow v = 2$
This is the required solution.

Note: Always remember when you move any term from one side to the another, then the sign of the term also changes. Positive terms become negative and the negative term becomes positive. Also, be careful about the sign convention while simplifying like terms with the same or the different signs that are plus or minus.