Solve 1.5(x-2)-2.1 < 1.3(x-1)+2.5 | 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

$$1.5(x-2)-2.1 < 1.3(x-1)+2.5$$

Solve for x

$x<31.5$

Solution Steps

Use the distributive property to multiply $1.5$ by $x-2$.

$$1.5x-3-2.1<1.3\left(x-1\right)+2.5$$

Subtract $2.1$ from $-3$ to get $-5.1$.

$$1.5x-5.1<1.3\left(x-1\right)+2.5$$

Use the distributive property to multiply $1.3$ by $x-1$.

$$1.5x-5.1<1.3x-1.3+2.5$$

Add $-1.3$ and $2.5$ to get $1.2$.

$$1.5x-5.1<1.3x+1.2$$

Subtract $1.3x$ from both sides.

$$1.5x-5.1-1.3x<1.2$$

Combine $1.5x$ and $-1.3x$ to get $0.2x$.

$$0.2x-5.1<1.2$$

Add $5.1$ to both sides.

$$0.2x<1.2+5.1$$

Add $1.2$ and $5.1$ to get $6.3$.

$$0.2x<6.3$$

Divide both sides by $0.2$. Since $0.2$ is positive, the inequality direction remains the same.

$$x<\frac{6.3}{0.2}$$

Expand $\frac{6.3}{0.2}$ by multiplying both numerator and the denominator by $10$.

$$x<\frac{63}{2}$$