Exercise 1.1
Question 1: Represent each number on the number line.
\((i)\) \(\quad \frac{3}{4} \)
\((ii)\) \(\quad -\frac{1}{3} \)
\((iii)\) \(\quad 4\frac{1}{2} \)
\((iv)\) \(\quad -\sqrt{8} \)
\((v)\) \(\quad \sqrt{8} \)
\((vi)\) \(\quad -4\frac{1}{2} \)
\((vii)\) \(\quad \frac{1}{3} \)
\((viii)\) \(\quad -\frac{7}{8} \)
Question 2: Identify the property that justifies.
\((i)\) \(\quad 1\times \left( y-2 \right)=y-2 \)
\((ii)\) \(\quad \left( 0.2 \right)5=1 \)
\((iii) \quad \left( x+2 \right)+y=y+\left( x+2 \right) \)
\((iv) \quad -\left( 3b \right)+\left( 3b \right)=0 \)
\((v) \quad \left( x+5 \right)-1=x+\left( 5-1 \right) \)
\((vi) \quad -3\left( 2-y \right)=-6+3y \)
Question 3: Represent the following on a number line.
\((i)\) \(\quad x<0 \)
\((ii) \quad -3<x<3 \)
\((iii) \quad x\ge -8 \)
\((iv) \quad x>0 \)
\((v) \quad x<-3 \)
\((vi) \quad -4<x\le 4 \)
Question 4: Identify the properties of equality and inequality of real numbers that justifies the statement.
\((i)\) \(\quad 9x=9x \)
\((ii) \quad \text{If }x+2=y \)\(\text{ and }\)\(y=2x,\text{ then }x+2=2x-3 \)
\((iii) \quad \text{If 2}x+3=y,\text{ then }y=2x+3 \)
\((iv) \quad \text{If }3<4,\text{ then }-3>-4 \)
\((v) \quad \text{If }2y+2w=p\text{ and }p=50,\)\(\text{ then }\)\(2y+2w=50 \)
\((vi) \quad \text{If }x+4>y+4,\text{ then }x>y \)
\((vii) \quad \text{If }2<5\text{ and }5<9,\text{ then }2<9 \)
\((viii) \quad \text{If }-18<-16,\text{ then }9>8 \)