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QuestionSolve the equation −19(z+3)=−23(z−23)-\frac{1}{9}(z+3)=-\frac{2}{3}\left(z-\frac{2}{3}\right) and simplify to an integer, fraction, or decimal.

Studdy Solution

STEP 1

Assumptions1. The equation is a linear equation in variable z. . We need to solve for z.
3. The solution should be expressed as an integer, a simplified fraction, or a decimal rounded to two decimal places.

STEP 2

First, distribute the negative fraction on both sides of the equation.
−19z−1=−2z+29-\frac{1}{9}z - \frac{1}{} = -\frac{2}{}z + \frac{2}{9}

STEP 3

Next, we will isolate the variable z on one side of the equation. We can do this by adding 23z\frac{2}{3}z to both sides of the equation.
−19z+23z=−13+29-\frac{1}{9}z + \frac{2}{3}z = -\frac{1}{3} + \frac{2}{9}

STEP 4

Now, we will simplify the left side of the equation by combining like terms.
9z=−13+29\frac{}{9}z = -\frac{1}{3} + \frac{2}{9}

STEP 5

Next, we will simplify the right side of the equation by combining like terms.
59z=−13+29=−19\frac{5}{9}z = -\frac{1}{3} + \frac{2}{9} = -\frac{1}{9}

STEP 6

Now, we will solve for z by multiplying both sides of the equation by 95\frac{9}{5}.
z=95×−19z = \frac{9}{5} \times -\frac{1}{9}

STEP 7

Finally, we will simplify the right side of the equation to find the solution for z.
z=−15z = -\frac{1}{5}So, the solution to the equation is z=−15z = -\frac{1}{5}.

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