Solve (0.4z - 3)/(19 - 3y) = 5/8 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{0.4z-3}{19-3y}=\frac{5}{8}$$

Solve for y

$y=-\frac{16z}{75}+\frac{119}{15}$
$z\neq \frac{15}{2}$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $\frac{19}{3}$ since division by zero is not defined. Multiply both sides of the equation by $8\left(3y-19\right)$, the least common multiple of $19-3y,8$.

$$-8\left(0.4z-3\right)=5\left(3y-19\right)$$

Use the distributive property to multiply $-8$ by $0.4z-3$.

$$-3.2z+24=5\left(3y-19\right)$$

Use the distributive property to multiply $5$ by $3y-19$.

$$-3.2z+24=15y-95$$

Swap sides so that all variable terms are on the left hand side.

$$15y-95=-3.2z+24$$

Add $95$ to both sides.

$$15y=-3.2z+24+95$$

Add $24$ and $95$ to get $119$.

$$15y=-3.2z+119$$

The equation is in standard form.

$$15y=-\frac{16z}{5}+119$$

Divide both sides by $15$.

$$\frac{15y}{15}=\frac{-\frac{16z}{5}+119}{15}$$

Dividing by $15$ undoes the multiplication by $15$.

$$y=\frac{-\frac{16z}{5}+119}{15}$$

Divide $-\frac{16z}{5}+119$ by $15$.

$$y=-\frac{16z}{75}+\frac{119}{15}$$

Variable $y$ cannot be equal to $\frac{19}{3}$.

$$y=-\frac{16z}{75}+\frac{119}{15}\text{, }y\neq \frac{19}{3}$$

Solve for z

$z=\frac{595-75y}{16}$
$y\neq \frac{19}{3}$

Steps for Solving Linear Equation

Multiply both sides of the equation by $8\left(3y-19\right)$, the least common multiple of $19-3y,8$.

$$-8\left(0.4z-3\right)=5\left(3y-19\right)$$

Use the distributive property to multiply $-8$ by $0.4z-3$.

$$-3.2z+24=5\left(3y-19\right)$$

Use the distributive property to multiply $5$ by $3y-19$.

$$-3.2z+24=15y-95$$

Subtract $24$ from both sides.

$$-3.2z=15y-95-24$$

Subtract $24$ from $-95$ to get $-119$.

$$-3.2z=15y-119$$

Divide both sides of the equation by $-3.2$, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-3.2z}{-3.2}=\frac{15y-119}{-3.2}$$

Dividing by $-3.2$ undoes the multiplication by $-3.2$.

$$z=\frac{15y-119}{-3.2}$$

Divide $15y-119$ by $-3.2$ by multiplying $15y-119$ by the reciprocal of $-3.2$.

$$z=\frac{595-75y}{16}$$