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Class 9Class 10First YearSecond Year
Example 3Solve the double inequality -2<\frac{1-2 x}{3}<1 where x \in \mathrm{R} .
Example 3Solve the double inequality  -2<\frac{1-2 x}{3}<1  where  x \in \mathrm{R} .

Example 3Solve the double inequality -2<\frac{1-2 x}{3}<1 where x \in \mathrm{R} .

Example 2Solve \frac{1}{2} x-\frac{2}{3} \leq x+\frac{1}{3} where x \in \mathrm{R} .
Example 2Solve  \frac{1}{2} x-\frac{2}{3} \leq x+\frac{1}{3}  where  x \in \mathrm{R} .

Example 2Solve \frac{1}{2} x-\frac{2}{3} \leq x+\frac{1}{3} where x \in \mathrm{R} .

1. Solve the following equations.(x) \frac{2}{3 x+6}=\frac{1}{6}-\frac{1}{2 x+4} x \neq-2
1. Solve the following equations.(x)  \frac{2}{3 x+6}=\frac{1}{6}-\frac{1}{2 x+4} x \neq-2

1. Solve the following equations.(x) \frac{2}{3 x+6}=\frac{1}{6}-\frac{1}{2 x+4} x \neq-2

1. Solve the following equations.(vi) \frac{x}{3 x-6}=2-\frac{2 x}{x-2} x \neq 2
1. Solve the following equations.(vi)  \frac{x}{3 x-6}=2-\frac{2 x}{x-2} x \neq 2

1. Solve the following equations.(vi) \frac{x}{3 x-6}=2-\frac{2 x}{x-2} x \neq 2

3. Answer the following short questions.(iv) Seven times the sum of an integer and 12 is at least 50 and at most 60 . Write and solve the inequality that expresses this relationship.
3. Answer the following short questions.(iv) Seven times the sum of an integer and 12 is at least 50 and at most 60 . Write and solve the inequality that expresses this relationship.

3. Answer the following short questions.(iv) Seven times the sum of an integer and 12 is at least 50 and at most 60 . Write and solve the inequality that expresses this relationship.

2. Solve for x (vi) \frac{1}{2}|x+3|+21=9
2. Solve for  x (vi)  \frac{1}{2}|x+3|+21=9

2. Solve for x (vi) \frac{1}{2}|x+3|+21=9

2. Solve for x (viii) \left|\frac{x+5}{2-x}\right|=6
2. Solve for  x (viii)  \left|\frac{x+5}{2-x}\right|=6

2. Solve for x (viii) \left|\frac{x+5}{2-x}\right|=6

3. Answer the following short questions.(ii) State the trichotomy and transitive properties of inequalities.
3. Answer the following short questions.(ii) State the trichotomy and transitive properties of inequalities.

3. Answer the following short questions.(ii) State the trichotomy and transitive properties of inequalities.

(vi) x=0 is a solution of the inequality(a) x>0 (b) 3 x+5<0 (c) x+2<0 (d) x-2<0
(vi)  x=0  is a solution of the inequality(a)  x>0 (b)  3 x+5<0 (c)  x+2<0 (d)  x-2<0

(vi) x=0 is a solution of the inequality(a) x>0 (b) 3 x+5<0 (c) x+2<0 (d) x-2<0

6. Solve the following inequality(ii) -3<\frac{1-2 x}{5}<1
6. Solve the following inequality(ii)  -3<\frac{1-2 x}{5}<1

6. Solve the following inequality(ii) -3<\frac{1-2 x}{5}<1

Example 3\[\text { Solve } \frac{3 x-1}{3}-\frac{2 x}{x-1}=x x \neq 1\]
Example 3\[\text { Solve } \frac{3 x-1}{3}-\frac{2 x}{x-1}=x  x \neq 1\]

Example 3\[\text { Solve } \frac{3 x-1}{3}-\frac{2 x}{x-1}=x x \neq 1\]

2. Solve each equation and check for extraneous solution if any.(vii) \sqrt{2 t+6}-\sqrt{2 t-5}=0
2. Solve each equation and check for extraneous solution if any.(vii)  \sqrt{2 t+6}-\sqrt{2 t-5}=0

2. Solve each equation and check for extraneous solution if any.(vii) \sqrt{2 t+6}-\sqrt{2 t-5}=0

(v) If the capacity c of an elevator is at most 1600 pounds then .......(a) c<1600 (b) c \geq 1600 (c) c \leq 1600 (d) c>1600
(v) If the capacity  c  of an elevator is at most 1600 pounds then .......(a)  c<1600 (b)  c \geq 1600 (c)  c \leq 1600 (d)  c>1600

(v) If the capacity c of an elevator is at most 1600 pounds then .......(a) c<1600 (b) c \geq 1600 (c) c \leq 1600 (d) c>1600

1. Solve the following equations.(iv) x+\frac{1}{3}=2\left(x-\frac{2}{3}\right)-6 x
1. Solve the following equations.(iv)  x+\frac{1}{3}=2\left(x-\frac{2}{3}\right)-6 x

1. Solve the following equations.(iv) x+\frac{1}{3}=2\left(x-\frac{2}{3}\right)-6 x

Example 2Solve \frac{3}{y-1}-2=\frac{3 y}{y-1} y \neq 1
Example 2Solve  \frac{3}{y-1}-2=\frac{3 y}{y-1}  y \neq 1

Example 2Solve \frac{3}{y-1}-2=\frac{3 y}{y-1} y \neq 1

2. Solve each equation and check for extraneous solution if any.(vi) \sqrt[3]{2-t}=\sqrt[3]{2 t-28}
2. Solve each equation and check for extraneous solution if any.(vi)  \sqrt[3]{2-t}=\sqrt[3]{2 t-28}

2. Solve each equation and check for extraneous solution if any.(vi) \sqrt[3]{2-t}=\sqrt[3]{2 t-28}

2. Solve each equation and check for extraneous solution if any.(v) \sqrt[3]{2 x+3}=\sqrt[3]{x-2}
2. Solve each equation and check for extraneous solution if any.(v)  \sqrt[3]{2 x+3}=\sqrt[3]{x-2}

2. Solve each equation and check for extraneous solution if any.(v) \sqrt[3]{2 x+3}=\sqrt[3]{x-2}

2. Solve each equation and check for extraneous solution if any.(i) \sqrt{3 x+4}=2
2. Solve each equation and check for extraneous solution if any.(i)  \sqrt{3 x+4}=2

2. Solve each equation and check for extraneous solution if any.(i) \sqrt{3 x+4}=2

Example 1Solve the equations(a) \sqrt{2 x-3}-7=0 (b) \sqrt[3]{3 x+5}=\sqrt[3]{x-1}
Example 1Solve the equations(a)  \sqrt{2 x-3}-7=0 (b)  \sqrt[3]{3 x+5}=\sqrt[3]{x-1}
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Example 1Solve the equations(a) \sqrt{2 x-3}-7=0 (b) \sqrt[3]{3 x+5}=\sqrt[3]{x-1}

5. Solve for x (i) |3 x+14|-2=5 x
5. Solve for  x (i)  |3 x+14|-2=5 x
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5. Solve for x (i) |3 x+14|-2=5 x

(iv) If x is no larger than 10 then \ldots \ldots . (a) x \geq 8 (b) x \leq 10 (c) x<10 (d) x>10
(iv) If  x  is no larger than 10 then  \ldots \ldots . (a)  x \geq 8 (b)  x \leq 10 (c)  x<10 (d)  x>10
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(iv) If x is no larger than 10 then \ldots \ldots . (a) x \geq 8 (b) x \leq 10 (c) x<10 (d) x>10

1. Solve the following equations.(v) \frac{5(x-3)}{6}-x=1-\frac{x}{9}
1. Solve the following equations.(v)  \frac{5(x-3)}{6}-x=1-\frac{x}{9}
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1. Solve the following equations.(v) \frac{5(x-3)}{6}-x=1-\frac{x}{9}

Example 1Solve the equation \frac{3 x}{2}-\frac{x-2}{3}=\frac{25}{6}
Example 1Solve the equation  \frac{3 x}{2}-\frac{x-2}{3}=\frac{25}{6}
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Example 1Solve the equation \frac{3 x}{2}-\frac{x-2}{3}=\frac{25}{6}

1. Solve the following equations.(viii) \frac{2 x}{x-1}+\frac{1}{3}=\frac{5}{6}+\frac{2}{x-1} x \neq 1
1. Solve the following equations.(viii)  \frac{2 x}{x-1}+\frac{1}{3}=\frac{5}{6}+\frac{2}{x-1} x \neq 1
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1. Solve the following equations.(viii) \frac{2 x}{x-1}+\frac{1}{3}=\frac{5}{6}+\frac{2}{x-1} x \neq 1

3. Answer the following short questions.(iii) The formula relating degrees Fahrenheit to degrees Celsius is \mathrm{F}=\frac{9}{5} \mathrm{C}+32 . For what value of \mathrm{C} is \mathrm{F}<0 ?
3. Answer the following short questions.(iii) The formula relating degrees Fahrenheit to degrees Celsius is  \mathrm{F}=\frac{9}{5} \mathrm{C}+32 . For what value of  \mathrm{C}  is  \mathrm{F}<0  ?
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3. Answer the following short questions.(iii) The formula relating degrees Fahrenheit to degrees Celsius is \mathrm{F}=\frac{9}{5} \mathrm{C}+32 . For what value of \mathrm{C} is \mathrm{F}<0 ?

2. Solve for x (iii) |2 x+5|=11
2. Solve for  x (iii)  |2 x+5|=11
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2. Solve for x (iii) |2 x+5|=11

2. Solve each equation and check for extraneous solution if any.(iv) 2 \sqrt{t+4}=5
2. Solve each equation and check for extraneous solution if any.(iv)  2 \sqrt{t+4}=5
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2. Solve each equation and check for extraneous solution if any.(iv) 2 \sqrt{t+4}=5

3. Answer the following short questions.(i) Define a linear inequality in one variable.
3. Answer the following short questions.(i) Define a linear inequality in one variable.
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3. Answer the following short questions.(i) Define a linear inequality in one variable.

5. Solve for x (ii) \frac{1}{3}|x-3|=\frac{1}{2}|x+2|
5. Solve for  x (ii)  \frac{1}{3}|x-3|=\frac{1}{2}|x+2|
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5. Solve for x (ii) \frac{1}{3}|x-3|=\frac{1}{2}|x+2|