Solve the following system of linear inequalities and represent the solution graphically on a number line:
$3x - 7 > 2(x - 6), 6 - x > 11 - 2x$
$3x - 7 > 2(x - 6), 6 - x > 11 - 2x$
(N/A) First,solve the first inequality:
$3x - 7 > 2(x - 6)$
$3x - 7 > 2x - 12$
$3x - 2x > -12 + 7$
$x > -5$ ..... $(1)$
Next,solve the second inequality:
$6 - x > 11 - 2x$
$-x + 2x > 11 - 6$
$x > 5$ ..... $(2)$
From $(1)$ and $(2)$,the common solution is the intersection of the two intervals,which is $x > 5$.
Thus,the solution set is $(5, \infty)$.
The graphical representation on the number line is shown below:
$3x - 7 > 2(x - 6)$
$3x - 7 > 2x - 12$
$3x - 2x > -12 + 7$
$x > -5$ ..... $(1)$
Next,solve the second inequality:
$6 - x > 11 - 2x$
$-x + 2x > 11 - 6$
$x > 5$ ..... $(2)$
From $(1)$ and $(2)$,the common solution is the intersection of the two intervals,which is $x > 5$.
Thus,the solution set is $(5, \infty)$.
The graphical representation on the number line is shown below:
Explore More
Similar Questions
Solve $3x + 8 > 2$,when $x$ is an integer.
Easy
View SolutionThe set $A = \{x : |2x + 3| < 7\}$ is equal to which of the following sets?
Solve the following inequality and represent it on a number line: $\frac{x-1}{2}+5 \geq \frac{2x-1}{3}+15$
Easy
View SolutionThe shaded region in the figure represents the $\ldots \ldots \ldots$ inequality.
Medium
View SolutionSolve the given inequality for real $x$: $x+\frac{x}{2}+\frac{x}{3} < 11$
Easy
View SolutionVedclass 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