Question

How do you solve $2(2x - 5) = 6x + 5$ ?

Answer 1

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 $(x + 3)(x - 8)$
Now we first start by opening the brackets and multiplying the terms.
$
 \Rightarrow 2(2x - 5) = 6x + 5 \\
 \Rightarrow 2(2x) - 2(5) = 6x + 5 \\
 $
Now we will simplify the terms.
$
 \Rightarrow 4x - 10 = 6x + 5 \\
 \Rightarrow - 5 - 10 = 6x - 4x \\
 $
Now we combine all the like terms together.
$
\Rightarrow - 5 - 10 = 6x - 4x \\
 \Rightarrow - 15 = 2x \\
\Rightarrow x = \dfrac{{ - 15}}{2} \\
 $
Hence, the simplified form of the expression $2(2x - 5) = 6x + 5$ is $\dfrac{{ - 15}}{2}$.
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. 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 evaluating such equations, make sure you first take down all the terms to their simpler forms, so that the equation becomes simpler to solve. Then next when you open the brackets always multiply all the terms inside the bracket with the sign present outside the bracket.