Solve (1-x)/(3) >= x-(4x-2)/(4) | 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

$$\frac{ 1-x }{ 3 } \geq x- \frac{ 4x-2 }{ 4 }$$

Solve for x

$x\leq -\frac{1}{2}$

Solution Steps

Multiply both sides of the equation by $12$, the least common multiple of $3,4$. Since $12$ is positive, the inequality direction remains the same.

$$4\left(1-x\right)\geq 12x-3\left(4x-2\right)$$

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

$$4-4x\geq 12x-3\left(4x-2\right)$$

Use the distributive property to multiply $-3$ by $4x-2$.

$$4-4x\geq 12x-12x+6$$

Combine $12x$ and $-12x$ to get $0$.

$$4-4x\geq 6$$

Subtract $4$ from both sides.

$$-4x\geq 6-4$$

Subtract $4$ from $6$ to get $2$.

$$-4x\geq 2$$

Divide both sides by $-4$. Since $-4$ is negative, the inequality direction is changed.

$$x\leq \frac{2}{-4}$$

Reduce the fraction $\frac{2}{-4}$ to lowest terms by extracting and canceling out $2$.

$$x\leq -\frac{1}{2}$$