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Solve for $z$ . $\newline$ $\frac{5}{3}z + 1 = 3 - \frac{2}{3}z$ $\newline$ $z =$ ____

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Solve equations with variables on both sides: fractional coefficients

Full solution

Q. Solve for

z

.

\newline

\frac{5}{3}z + 1 = 3 - \frac{2}{3}z

\newline

z =

____

Combine like terms: Combine like terms involving $z$ on both sides. $\newline$ $\frac{5}{3}z + 1 = 3 - \frac{2}{3}z$ $\newline$ $\frac{5}{3}z + \frac{2}{3}z = 3 - 1$
Simplify the equation: Simplify the equation by adding fractions. $\newline$ $(\frac{5}{3} + \frac{2}{3})z = 2$ $\newline$ $\frac{7}{3}z = 2$
Solve for $z$ : Solve for $z$ by multiplying both sides by the reciprocal of $\frac{7}{3}$ . $z = 2 \times \left(\frac{3}{7}\right)$ $z = \frac{6}{7}$

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