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How do you solve the two-step inequality $4x - 6 > 6x - 20$ ?

Last updated date: 18th Jun 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 answer:
 First we will start off by evaluating the inequality $4x - 6 > 6x - 20$
Now we subtract $4x$ from both the sides so we get,
$4x - 6 > 6x - 20 \\
\Rightarrow - 6 > 2x - 20$
Now we will add $20$ to both the sides.
$- 6 > 2x - 20 \\
\Rightarrow 14 > 2x $
Divide both the sides by $2$.
$7 > x$
Now if we reverse to a more standard form:
$x < 7$

Additional Information:
To cross multiply terms, you will multiply the numerator in the first fraction times the denominator in the second fraction, then you write that number down. Then you multiply the numerator of the second fraction times the number in the denominator of your first fraction, and then you write that number down.

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.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.