Solve 15(x-9)-2(x-12)+5(x+6)=0 | 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

$$15(x-9)-2(x-12)+5(x+6)=0$$

Solve for x

$x = \frac{9}{2} = 4\frac{1}{2} = 4.5$

Steps for Solving Linear Equation

Use the distributive property to multiply $15$ by $x-9$.

$$15x-135-2\left(x-12\right)+5\left(x+6\right)=0$$

Use the distributive property to multiply $-2$ by $x-12$.

$$15x-135-2x+24+5\left(x+6\right)=0$$

Combine $15x$ and $-2x$ to get $13x$.

$$13x-135+24+5\left(x+6\right)=0$$

Add $-135$ and $24$ to get $-111$.

$$13x-111+5\left(x+6\right)=0$$

Use the distributive property to multiply $5$ by $x+6$.

$$13x-111+5x+30=0$$

Combine $13x$ and $5x$ to get $18x$.

$$18x-111+30=0$$

Add $-111$ and $30$ to get $-81$.

$$18x-81=0$$

Add $81$ to both sides. Anything plus zero gives itself.

$$18x=81$$

Divide both sides by $18$.

$$x=\frac{81}{18}$$

Reduce the fraction $\frac{81}{18}$ to lowest terms by extracting and canceling out $9$.

$$x=\frac{9}{2}$$