1) What is the value of x in the equation 1 8/27 divided by x equals - 1 5/9? 2) If the equation - 2 5/8 divided

Svetlyy_Angel

39

Sure, I can help you with that. Let"s solve these two equations step by step:

1) What is the value of \(x\) in the equation \(\frac{{18}}{{27}} \div x = - \frac{{1}}{{5}}\frac{{9}}{{9}}\)?

To solve this equation, we need to isolate the variable \(x\) on one side of the equation.

Step 1: Simplify the equation by dividing the fraction on the left-hand side.
\(\frac{{2}}{{3}} \div x = - \frac{{14}}{{9}}\)

Step 2: To get rid of the fraction, we can multiply both sides of the equation by the reciprocal of \(\frac{{2}}{{3}}\), which is \(\frac{{3}}{{2}}\).
\(x \times \frac{{3}}{{2}} = - \frac{{14}}{{9}} \times \frac{{3}}{{2}}\)

Step 3: Simplify the equation by performing the multiplication.
\(\frac{{3}}{{2}}x = - \frac{{21}}{{6}}\)

Step 4: To simplify further, we can divide both sides of the equation by \(\frac{{3}}{{2}}\).
\(x = - \frac{{21}}{{6}} \times \frac{{2}}{{3}}\)

Step 5: Simplify the equation by performing the multiplication.
\(x = - \frac{{7}}{{2}}\)

Therefore, the value of \(x\) in the given equation is \(- \frac{{7}}{{2}}\).

2) If the equation \(- \frac{{5}}{{8}} \div x = \frac{{1}}{{19}} \frac{{20}}{{1}}\), what is the value of \(x\)?

To solve this equation, we will follow a similar step-by-step approach.

Step 1: Simplify the equation by dividing the fraction on the left-hand side.
\(- \frac{{5}}{{8}} \div x = \frac{{39}}{{20}}\)

Step 2: To eliminate the fraction, multiply both sides by the reciprocal of \(- \frac{{5}}{{8}}\), which is \(- \frac{{8}}{{5}}\).
\(x \times - \frac{{8}}{{5}} = \frac{{39}}{{20}} \times - \frac{{8}}{{5}}\)

Step 3: Simplify the equation by performing the multiplication.
\(- \frac{{8}}{{5}}x = - \frac{{312}}{{100}}\)

Step 4: To simplify further, divide both sides of the equation by \(- \frac{{8}}{{5}}\).
\(x = - \frac{{312}}{{100}} \div - \frac{{8}}{{5}}\)

Step 5: Simplify the equation by performing the division.
\(x = \frac{{312}}{{100}} \times \frac{{5}}{{8}}\)

Step 6: Simplify the equation by canceling out common factors.
\(x = \frac{{39}}{{10}}\)

Therefore, the value of \(x\) in the given equation is \(\frac{{39}}{{10}}\).