Math  /  Algebra

Question竣, Spolve for zz. 23z=2+32z12z=\begin{array}{l} \frac{2}{3} z=2+\frac{3}{2} z-\frac{1}{2} \\ z=\square \end{array} Submit

Studdy Solution
Calculate each term:
Left side:
23×95=1815=65 \frac{2}{3} \times -\frac{9}{5} = -\frac{18}{15} = -\frac{6}{5}
Right side:
2+32×9512=2271012 2 + \frac{3}{2} \times -\frac{9}{5} - \frac{1}{2} = 2 - \frac{27}{10} - \frac{1}{2}
Convert to a common denominator (10):
2=2010,12=510 2 = \frac{20}{10}, \quad -\frac{1}{2} = -\frac{5}{10}
20102710510=2027510=1210=65 \frac{20}{10} - \frac{27}{10} - \frac{5}{10} = \frac{20 - 27 - 5}{10} = -\frac{12}{10} = -\frac{6}{5}
Both sides are equal, confirming the solution is correct.
The solution is:
z=95 z = -\frac{9}{5}

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