Solve $7x + 3 < 5x + 9$. Show the graph of the solutions on a number line.
(N/A) Given inequality: $7x + 3 < 5x + 9$
Subtract $5x$ from both sides: $2x + 3 < 9$
Subtract $3$ from both sides: $2x < 6$
Divide by $2$: $x < 3$
The solution set is all real numbers less than $3$. The graphical representation on the number line is a ray starting from $3$ (with an open circle at $3$ to indicate that $3$ is not included) extending to the left towards negative infinity.
Subtract $5x$ from both sides: $2x + 3 < 9$
Subtract $3$ from both sides: $2x < 6$
Divide by $2$: $x < 3$
The solution set is all real numbers less than $3$. The graphical representation on the number line is a ray starting from $3$ (with an open circle at $3$ to indicate that $3$ is not included) extending to the left towards negative infinity.
Explore More
Similar Questions
Solve $\frac{3x-4}{2} \geq \frac{x+1}{4}-1$. Show the graph of the solutions on a number line.
Medium
View SolutionSolve $(8-t)^2 < (t^2-3t-10)$
Solve the given inequality graphically in a two-dimensional plane: $3y - 5x < 30$
Easy
View SolutionSolve the inequalities for real $x$: $\frac{5-3x}{3} \leq \frac{x}{6}-5$.
Easy
View SolutionConsider the following statements :
Statement $(I)$ : The set of all solutions of the linear inequalities $3x + 8 < 17$ and $2x + 8 \geq 12$ are $x < 3$ and $x \geq 2$ respectively.
Statement $(II)$ : The common set of solutions of linear inequalities $3x + 8 < 17$ and $2x + 8 \geq 12$ is $(2, 3)$.
Which of the following is true?
Statement $(I)$ : The set of all solutions of the linear inequalities $3x + 8 < 17$ and $2x + 8 \geq 12$ are $x < 3$ and $x \geq 2$ respectively.
Statement $(II)$ : The common set of solutions of linear inequalities $3x + 8 < 17$ and $2x + 8 \geq 12$ is $(2, 3)$.
Which of the following is true?
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo