Solve (3x - 5)/2 - (4x + 5)/5 = 3/4 + x | 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

$$\frac{3x-5}{2}-\frac{4x+5}{5}=\frac{3}{4}+x$$

Solve for x

$x = -\frac{85}{6} = -14\frac{1}{6} \approx -14.166666667$

Steps for Solving Linear Equation

Multiply both sides of the equation by $20$, the least common multiple of $2,5,4$.

$$10\left(3x-5\right)-4\left(4x+5\right)=15+20x$$

Use the distributive property to multiply $10$ by $3x-5$.

$$30x-50-4\left(4x+5\right)=15+20x$$

Use the distributive property to multiply $-4$ by $4x+5$.

$$30x-50-16x-20=15+20x$$

Combine $30x$ and $-16x$ to get $14x$.

$$14x-50-20=15+20x$$

Subtract $20$ from $-50$ to get $-70$.

$$14x-70=15+20x$$

Subtract $20x$ from both sides.

$$14x-70-20x=15$$

Combine $14x$ and $-20x$ to get $-6x$.

$$-6x-70=15$$

Add $70$ to both sides.

$$-6x=15+70$$

Add $15$ and $70$ to get $85$.

$$-6x=85$$

Divide both sides by $-6$.

$$x=\frac{85}{-6}$$

Fraction $\frac{85}{-6}$ can be rewritten as $-\frac{85}{6}$ by extracting the negative sign.

$$x=-\frac{85}{6}$$