Solve 9=(1)/(2)|2x-24+6+x-4-2| | 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

$$9= \frac{ 1 }{ 2 } |2x-24+6+x-4-2|$$

Solve for x

$x=2$
$x=14$

Steps Using Definition of Absolute Value

Multiply both sides by $2$, the reciprocal of $\frac{1}{2}$.

$$9\times 2=|2x-24+6+x-4-2|$$

Multiply $9$ and $2$ to get $18$.

$$18=|2x-24+6+x-4-2|$$

Add $-24$ and $6$ to get $-18$.

$$18=|2x-18+x-4-2|$$

Combine $2x$ and $x$ to get $3x$.

$$18=|3x-18-4-2|$$

Subtract $4$ from $-18$ to get $-22$.

$$18=|3x-22-2|$$

Subtract $2$ from $-22$ to get $-24$.

$$18=|3x-24|$$

Swap sides so that all variable terms are on the left hand side.

$$|3x-24|=18$$

Use the definition of absolute value.

$$3x-24=18$$ $$3x-24=-18$$

Add $24$ to both sides of the equation.

$$3x=42$$ $$3x=6$$

Divide both sides by $3$.

$$x=14$$ $$x=2$$