Question

How do you solve and check your solutions to \[\dfrac{8}{5}x = \dfrac{4}{{15}}\]?

Answer 1

Hint: To solve the given expression, we need to multiply each side of the equation by \[\dfrac{5}{8}\] to obtain the value of x and to keep the equation balanced and then we need to substitute the value of x in the given expression to check the solutions and ensure that both sides of the equation are equal.

Complete step by step solution:
Given,
\[\dfrac{8}{5}x = \dfrac{4}{{15}}\]
Multiply each side of the equation by \[\dfrac{5}{8}\]; to solve for x and to keep the equation balanced:
\[ \Rightarrow \dfrac{5}{8} \times \dfrac{8}{5}x = \dfrac{5}{8} \times \dfrac{4}{{15}}\]
Now, combine the terms to multiply as:
\[ \Rightarrow \dfrac{{5 \times 8}}{{8 \times 5}}x = \dfrac{{5 \times 4}}{{8 \times 15}}\]
Multiplying the terms, we get:
\[ \Rightarrow \dfrac{{40}}{{40}}x = \dfrac{{20}}{{120}}\]
Simplifying the numerator and denominator terms, we get:
\[ \Rightarrow x = \dfrac{1}{6}\]
To check the solution substitute \[\dfrac{1}{6}\] for x in the original equation and ensure both sides of the equation are equal then substituting the value of x in \[\dfrac{8}{5}x = \dfrac{4}{{15}}\], we have:
\[ \Rightarrow \dfrac{8}{5} \times \dfrac{1}{6} = \dfrac{4}{{15}}\]
Multiplying the terms, we have:
\[ \Rightarrow \dfrac{{8 \times 1}}{{5 \times 6}} = \dfrac{4}{{15}}\]
\[ \Rightarrow \dfrac{8}{{30}} = \dfrac{4}{{15}}\]
Evaluating the terms, we get:
\[ \Rightarrow \dfrac{4}{{15}} = \dfrac{4}{{15}}\]

Additional information:
A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true. To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself.

Note: The key point to solve these linear equations, is that we need to just simplify each side, if needed and then use Addition or Subtraction properties to move the variable term to one side and all other terms to the other side and then use multiplication and division to evaluate. You can note that for a one step equation to be completely solved, you only need a single step and that is, add or subtract and multiply or divide.