Solve x+1/2-5x+9/28=x+6/21+5-x-12/3 | 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

$$x+1/2-5x+9/28=x+6/21+5-x-12/3$$

Solve for x

$x=-\frac{13}{112}\approx -0.116071429$

Steps for Solving Linear Equation

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

$$-4x+\frac{1}{2}+\frac{9}{28}=x+\frac{6}{21}+5-x-\frac{12}{3}$$

Least common multiple of $2$ and $28$ is $28$. Convert $\frac{1}{2}$ and $\frac{9}{28}$ to fractions with denominator $28$.

$$-4x+\frac{14}{28}+\frac{9}{28}=x+\frac{6}{21}+5-x-\frac{12}{3}$$

Since $\frac{14}{28}$ and $\frac{9}{28}$ have the same denominator, add them by adding their numerators.

$$-4x+\frac{14+9}{28}=x+\frac{6}{21}+5-x-\frac{12}{3}$$

Add $14$ and $9$ to get $23$.

$$-4x+\frac{23}{28}=x+\frac{6}{21}+5-x-\frac{12}{3}$$

Reduce the fraction $\frac{6}{21}$ to lowest terms by extracting and canceling out $3$.

$$-4x+\frac{23}{28}=x+\frac{2}{7}+5-x-\frac{12}{3}$$

Convert $5$ to fraction $\frac{35}{7}$.

$$-4x+\frac{23}{28}=x+\frac{2}{7}+\frac{35}{7}-x-\frac{12}{3}$$

Since $\frac{2}{7}$ and $\frac{35}{7}$ have the same denominator, add them by adding their numerators.

$$-4x+\frac{23}{28}=x+\frac{2+35}{7}-x-\frac{12}{3}$$

Add $2$ and $35$ to get $37$.

$$-4x+\frac{23}{28}=x+\frac{37}{7}-x-\frac{12}{3}$$

Combine $x$ and $-x$ to get $0$.

$$-4x+\frac{23}{28}=\frac{37}{7}-\frac{12}{3}$$

Divide $12$ by $3$ to get $4$.

$$-4x+\frac{23}{28}=\frac{37}{7}-4$$

Convert $4$ to fraction $\frac{28}{7}$.

$$-4x+\frac{23}{28}=\frac{37}{7}-\frac{28}{7}$$

Since $\frac{37}{7}$ and $\frac{28}{7}$ have the same denominator, subtract them by subtracting their numerators.

$$-4x+\frac{23}{28}=\frac{37-28}{7}$$

Subtract $28$ from $37$ to get $9$.

$$-4x+\frac{23}{28}=\frac{9}{7}$$

Subtract $\frac{23}{28}$ from both sides.

$$-4x=\frac{9}{7}-\frac{23}{28}$$

Least common multiple of $7$ and $28$ is $28$. Convert $\frac{9}{7}$ and $\frac{23}{28}$ to fractions with denominator $28$.

$$-4x=\frac{36}{28}-\frac{23}{28}$$

Since $\frac{36}{28}$ and $\frac{23}{28}$ have the same denominator, subtract them by subtracting their numerators.

$$-4x=\frac{36-23}{28}$$

Subtract $23$ from $36$ to get $13$.

$$-4x=\frac{13}{28}$$

Divide both sides by $-4$.

$$x=\frac{\frac{13}{28}}{-4}$$

Express $\frac{\frac{13}{28}}{-4}$ as a single fraction.

$$x=\frac{13}{28\left(-4\right)}$$

Multiply $28$ and $-4$ to get $-112$.

$$x=\frac{13}{-112}$$

Fraction $\frac{13}{-112}$ can be rewritten as $-\frac{13}{112}$ by extracting the negative sign.

$$x=-\frac{13}{112}$$