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How do you solve multi-step equations?

Last updated date: 01st Mar 2024
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IVSAT 2024
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Hint: Take out all the like terms to one side and all the alike terms to the other side. Take out all the common terms. Reduce the terms on the both sides until they cannot be reduced any further if possible. Then finally evaluate the value of the unknown variable. Solve both the inequalities separately.

Complete step by step solution:
First we will start off by following the below steps:
(1) We start by first simplifying the expressions on each side of the equation if that is necessary, including combining all the like terms.
(2) Now next we will get all the variable terms on one side and all numbers on the other side using the additional property of equality which is $ax + b = c$ or $c = ax + b$.
(3) Further we will isolate the variable term using the inverse operation or additive inverse that is the opposite using the addition property of equality.
(4) Now in the next step we will isolate the variable using the inverse operation or multiplicative inverse that is the reciprocal using the multiplication property of equality to write the variable with a coefficient of $1$.
(5) Now finally check your solution by substituting the value of the variable in the original equality.

Additional Information: By Cross multiplication of fractions, we get to know if two fractions are equal or which one is greater. This is especially useful when you are working with larger fractions that you are not sure how to reduce. Cross multiplication also helps us to solve for unknown
variables in fractions.

Note: While cross multiplying the terms, multiply the terms step-by-step to avoid any mistakes. After cross multiplication, take the variables to one side and integer type of terms to the other side. Reduce the terms by factorisation.
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