Solve 1/(x - 1) + 1/2 = 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

$$\frac{1}{x-1}+\frac{1}{2}=\frac{5}{8}$$

Solve for x

$x=9$

Steps for Solving Linear Equation

Variable $x$ cannot be equal to $1$ since division by zero is not defined. Multiply both sides of the equation by $8\left(x-1\right)$, the least common multiple of $x-1,2,8$.

$$8+8\left(x-1\right)\times \frac{1}{2}=5\left(x-1\right)$$

Multiply $8$ and $\frac{1}{2}$ to get $4$.

$$8+4\left(x-1\right)=5\left(x-1\right)$$

Use the distributive property to multiply $4$ by $x-1$.

$$8+4x-4=5\left(x-1\right)$$

Subtract $4$ from $8$ to get $4$.

$$4+4x=5\left(x-1\right)$$

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

$$4+4x=5x-5$$

Subtract $5x$ from both sides.

$$4+4x-5x=-5$$

Combine $4x$ and $-5x$ to get $-x$.

$$4-x=-5$$

Subtract $4$ from both sides.

$$-x=-5-4$$

Subtract $4$ from $-5$ to get $-9$.

$$-x=-9$$

Multiply both sides by $-1$.

$$x=9$$