Solve (5(1 - u) + 3(1 + x))/(1 - 2x) = 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

$$\frac{5(1-u)+3(1+x)}{1-2x}=8$$

Solve for u

$u=\frac{19x}{5}$
$x\neq \frac{1}{2}$

Steps for Solving Linear Equation

Multiply both sides of the equation by $-2x+1$.

$$5\left(1-u\right)+3\left(1+x\right)=8\left(-2x+1\right)$$

Use the distributive property to multiply $5$ by $1-u$.

$$5-5u+3\left(1+x\right)=8\left(-2x+1\right)$$

Use the distributive property to multiply $3$ by $1+x$.

$$5-5u+3+3x=8\left(-2x+1\right)$$

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

$$8-5u+3x=8\left(-2x+1\right)$$

Use the distributive property to multiply $8$ by $-2x+1$.

$$8-5u+3x=-16x+8$$

Subtract $8$ from both sides.

$$-5u+3x=-16x+8-8$$

Subtract $8$ from $8$ to get $0$.

$$-5u+3x=-16x$$

Subtract $3x$ from both sides.

$$-5u=-16x-3x$$

Combine $-16x$ and $-3x$ to get $-19x$.

$$-5u=-19x$$

Divide both sides by $-5$.

$$\frac{-5u}{-5}=-\frac{19x}{-5}$$

Dividing by $-5$ undoes the multiplication by $-5$.

$$u=-\frac{19x}{-5}$$

Divide $-19x$ by $-5$.

$$u=\frac{19x}{5}$$

Solve for x

$x=\frac{5u}{19}$
$u\neq \frac{19}{10}$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $\frac{1}{2}$ since division by zero is not defined. Multiply both sides of the equation by $-2x+1$.

$$5\left(1-u\right)+3\left(1+x\right)=8\left(-2x+1\right)$$

Use the distributive property to multiply $5$ by $1-u$.

$$5-5u+3\left(1+x\right)=8\left(-2x+1\right)$$

Use the distributive property to multiply $3$ by $1+x$.

$$5-5u+3+3x=8\left(-2x+1\right)$$

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

$$8-5u+3x=8\left(-2x+1\right)$$

Use the distributive property to multiply $8$ by $-2x+1$.

$$8-5u+3x=-16x+8$$

Add $16x$ to both sides.

$$8-5u+3x+16x=8$$

Combine $3x$ and $16x$ to get $19x$.

$$8-5u+19x=8$$

Subtract $8$ from both sides.

$$-5u+19x=8-8$$

Subtract $8$ from $8$ to get $0$.

$$-5u+19x=0$$

Add $5u$ to both sides. Anything plus zero gives itself.

$$19x=5u$$

Divide both sides by $19$.

$$\frac{19x}{19}=\frac{5u}{19}$$

Dividing by $19$ undoes the multiplication by $19$.

$$x=\frac{5u}{19}$$

Variable $x$ cannot be equal to $\frac{1}{2}$.

$$x=\frac{5u}{19}\text{, }x\neq \frac{1}{2}$$