Note: This is the Solution of review exercise 5.1 from newly published book by PCTB (Punjab Curriculum and Textbook Board, Pakistan) for new 9th session 2025 Onward.
Exercise 5.1
Question # 01: Solve and represent the solution on a real line:
\((i)\) \(\quad\) \( 12x+30=-6\)
\((ii)\) \(\quad\) \(\frac{x}{3}+6=-12\)
\((iii)\) \(\quad\) \(\frac{x}{2}-\frac{3x}{4}=\frac{1}{12} \)
\((iv)\) \(\quad \)\(2=7(2x+4)+12x \)
\((v)\) \(\quad \) \(\frac{2x-1}{3}-\frac{3x}{4} =\frac{5}{6}\)
\((vi)\) \(\quad \) \(\frac{-5x}{10}=9-\frac{10}{5}x \)
Question 2: Solve each inequality and represent the solution on a real line.
\((i)\) \(\quad\) \( x-6\le -2\)
\((ii)\) \(\quad\) \(-9>-16+x\)
\((iii)\) \(\quad\) \(3+2x\ge 3 \)
\((iv)\) \(\quad \)\(6(x+10) \le 0 \)
\((v)\) \(\quad \)\(\frac{5}{3}x-\frac{3}{4}<-\frac{1}{12}\)
\((vi)\) \(\quad \)\(\frac{1}{4}x-\frac{1}{2}\le-1+\frac{1}{2}x\)
Question 3: Shade the solution region for the following linear inequalities in \(\small{xy-plane}\):
\((i)\) \(\quad\) \( 2x+y\le 6\)
\((ii)\) \(\quad\) \(3x+7y\ge 21 \)
\((iii)\) \(\quad\) \(3x-2y\ge 6 \)
\((iv)\) \(\quad \)\(5x-4y\le 20 \)
\((v)\) \(\quad \) \(2x+1\ge 0 \)
\((vi)\) \(\quad \) \(3y-4 \le 0 \)
Question 4: Indicate the solution region of the following linear inequalities by shading:
\((i)\) \(\quad\) \( 2x-3y \le 6\)
\(\qquad 2x+3y\le 12\)
\((ii)\) \(\quad\) \( x+y \ge 5\)
\(\qquad -y+x\le 1\)
\((iii)\) \(\quad\) \( 3x+7y \ge 21\)
\(\qquad x-y\le 2\)
\((iv)\) \(\quad\) \( 4x-3y \le 12\)
\(\qquad -x\ge -\frac{3}{2}\)
\((iii)\) \(\quad\) \( 3x+7y \ge 21\)
\(\qquad \quad y\le 4\)
\((iii)\) \(\quad\) \( 5x+7y \le 35\)
\(\qquad \quad x-2y\le 2\)