Solve the inequalities and represent the solution graphically on…

Question 35 of 40intermediate🔧 ApplyNumerical4 marks

Solve the inequalities and represent the solution graphically on number line: $3x - 7 > 2(x - 6), \quad 6 - x > 11 - 2x$

Correct Answer

The solution set is $(5, \infty)$ .

Exercise: Miscellaneous Exercise on Chapter 5 | Q: 9 | (Page Page 10)

For More Understanding

Explanation

This question involves solving a system of two linear inequalities and finding their common solution. Following the methodology shown in Example 11 of the textbook, we solve each inequality separately and then find the intersection of both solution sets. The key concept is that for a system of inequalities, the solution must satisfy ALL inequalities simultaneously.

Solution Steps

Step 1: Solve the first inequality
$3x - 7 > 2(x - 6)$ $3x - 7 > 2x - 12$ $3x - 2x > -12 + 7$ $x > -5$
The solution set is $(-5, \infty)$ .
Step 2: Solve the second inequality
$6 - x > 11 - 2x$ $-x + 2x > 11 - 6$ $x > 5$
The solution set is $(5, \infty)$ .
Step 3: Find the common solution From inequality (1): $x > -5$ From inequality (2): $x > 5$

Since both conditions must be satisfied simultaneously, and $x > 5$ is a subset of $x > -5$ , the common solution is $x > 5$ .

The solution set is $(5, \infty)$ .
Step 4: Graphical Representation on Number Line Draw a number line. Place an open circle at the point 5 (since 5 is not included in the solution). Draw a ray extending to the right from 5 towards infinity, indicating all real numbers greater than 5.

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