Solve 2x + 5 + 3 = 3x + mu*x - 1 | 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

$$2x+5+3=3x+\mu x-1$$

Solve for x

$x=\frac{9}{\mu +1}$
$\mu \neq -1$

Steps for Solving Linear Equation

Add $5$ and $3$ to get $8$.

$$2x+8=3x+\mu x-1$$

Subtract $3x$ from both sides.

$$2x+8-3x=\mu x-1$$

Combine $2x$ and $-3x$ to get $-x$.

$$-x+8=\mu x-1$$

Subtract $\mu x$ from both sides.

$$-x+8-\mu x=-1$$

Subtract $8$ from both sides.

$$-x-\mu x=-1-8$$

Subtract $8$ from $-1$ to get $-9$.

$$-x-\mu x=-9$$

Combine all terms containing $x$.

$$\left(-1-\mu \right)x=-9$$

The equation is in standard form.

$$\left(-\mu -1\right)x=-9$$

Divide both sides by $-\mu -1$.

$$\frac{\left(-\mu -1\right)x}{-\mu -1}=-\frac{9}{-\mu -1}$$

Dividing by $-\mu -1$ undoes the multiplication by $-\mu -1$.

$$x=-\frac{9}{-\mu -1}$$

Divide $-9$ by $-\mu -1$.

$$x=\frac{9}{\mu +1}$$

Solve for μ

$\mu =-1+\frac{9}{x}$
$x\neq 0$

Steps for Solving Linear Equation

Add $5$ and $3$ to get $8$.

$$2x+8=3x+\mu x-1$$

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

$$3x+\mu x-1=2x+8$$

Subtract $3x$ from both sides.

$$\mu x-1=2x+8-3x$$

Combine $2x$ and $-3x$ to get $-x$.

$$\mu x-1=-x+8$$

Add $1$ to both sides.

$$\mu x=-x+8+1$$

Add $8$ and $1$ to get $9$.

$$\mu x=-x+9$$

The equation is in standard form.

$$x\mu =9-x$$

Divide both sides by $x$.

$$\frac{x\mu }{x}=\frac{9-x}{x}$$

Dividing by $x$ undoes the multiplication by $x$.

$$\mu =\frac{9-x}{x}$$

Divide $-x+9$ by $x$.

$$\mu =-1+\frac{9}{x}$$