Solve (5)/(9)|2x-4|=(1)/(20) | 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

$$\frac{ 5 }{ 9 } |2x-4|= \frac{ 1 }{ 20 }$$

Solve for x

$x = \frac{391}{200} = 1\frac{191}{200} = 1.955$
$x = \frac{409}{200} = 2\frac{9}{200} = 2.045$

Steps Using Definition of Absolute Value

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

$$\frac{5}{9}|2x-4|=\frac{1}{20}$$

Divide both sides of the equation by $\frac{5}{9}$, which is the same as multiplying both sides by the reciprocal of the fraction.

$$|2x-4|=\frac{9}{100}$$

Use the definition of absolute value.

$$2x-4=\frac{9}{100}$$ $$2x-4=-\frac{9}{100}$$

Add $4$ to both sides of the equation.

$$2x=\frac{409}{100}$$ $$2x=\frac{391}{100}$$

Divide both sides by $2$.

$$x=\frac{409}{200}$$ $$x=\frac{391}{200}$$