How to solve 3z+2/3=5z-2/4

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 3z+2/3=5z-2/4 | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$3z+2/3=5z-2/4$$

Solve for z

$z=\frac{7}{12}\approx 0.583333333$

Steps for Solving Linear Equation

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

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

Subtract $5z$ from both sides.

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

Combine $3z$ and $-5z$ to get $-2z$.

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

Subtract $\frac{2}{3}$ from both sides.

$$-2z=-\frac{1}{2}-\frac{2}{3}$$

Least common multiple of $2$ and $3$ is $6$. Convert $-\frac{1}{2}$ and $\frac{2}{3}$ to fractions with denominator $6$.

$$-2z=-\frac{3}{6}-\frac{4}{6}$$

Since $-\frac{3}{6}$ and $\frac{4}{6}$ have the same denominator, subtract them by subtracting their numerators.

$$-2z=\frac{-3-4}{6}$$

Subtract $4$ from $-3$ to get $-7$.

$$-2z=-\frac{7}{6}$$

Divide both sides by $-2$.

$$z=\frac{-\frac{7}{6}}{-2}$$

Express $\frac{-\frac{7}{6}}{-2}$ as a single fraction.

$$z=\frac{-7}{6\left(-2\right)}$$

Multiply $6$ and $-2$ to get $-12$.

$$z=\frac{-7}{-12}$$

Fraction $\frac{-7}{-12}$ can be simplified to $\frac{7}{12}$ by removing the negative sign from both the numerator and the denominator.

$$z=\frac{7}{12}$$

Show Solution