[5 marks sum]

Question 15 Marks

Solve and graph the solution set on a number line : $\frac{x}{2}>-1+\frac{3 x}{4} ; x \in N$

Answer

$\frac{x}{2}>-1+\frac{3 x}{4}$
$\Rightarrow \frac{\mathrm{x}}{2} \times 4>-1 \times 4+\frac{3 \mathrm{x}}{4} \times 4..($Multiplying both sides by $4 )$
$\Rightarrow 2 x>-4+3 x$
$\Rightarrow 2 \mathrm{x}-2 \mathrm{x}>-4+3 \mathrm{x}-2 \mathrm{x}...($Subtracting $2 \mathrm{x}$ from both sides$)$
$\Rightarrow 0>-4+x$
$\Rightarrow 0+4>-4+4+x \ldots ($Adding $4$ to both sides$)$
$\Rightarrow 4>x$
$\therefore$ The required graph is :

View full question & answer→

Question 25 Marks

Solve and graph the solution set on a number line : $\frac{2 \mathrm{x}}{5}+1<-3 ; \mathrm{x} \in \mathrm{R}$

Answer

$\frac{2 \mathrm{x}}{5}+1<-3$
$ \Rightarrow \frac{2 \mathrm{x}}{5}+1-1<-3-1 ($Subtracting $1$ from both sides$)$
$ \Rightarrow \frac{2 \mathrm{x}}{5}<-4$
$ \Rightarrow \frac{2 \mathrm{x}}{5} \times 5<-4 \times 5 \ldots($ Multiplying both sides by $5)$
$ \Rightarrow 2 \mathrm{x}<-20$
$ \Rightarrow \frac{2 \mathrm{x}}{2}<\frac{-20}{2} \ldots ($Dividing both sides by $2)$
$ \Rightarrow \mathrm{x}<-10$
$\therefore$ The required graph is :

View full question & answer→

Question 35 Marks

Solve and graph the solution set on a number line : $5x + 4 > 8x – 11 ; x \in Z$

Answer

$5 x+4>8 x-11$
$\Rightarrow 5 x-5 x+4>8 x-5 x-11..($Subtracting $5 x$ from both sides$)$
$\Rightarrow 4>3 x-11$
$\Rightarrow 4+11>3 x-11+11...($Adding $11$ to both sides$)$
$\Rightarrow 15>3 x$
$\Rightarrow \frac{15}{3}>\frac{3 \mathrm{x}}{3} \ldots ($Dividing both sides by $3 )$
$\Rightarrow 5>x$
$\therefore$ The required graph is:

View full question & answer→

Question 45 Marks

Solve and graph the solution set on a number line : $8x – 9 > 35 – 3x ; x \in N$

Answer

$8 x-9 \geq 35-3 x$
$ \Rightarrow 8 x+3 x-9 \geq 35-3 x+3 x \ldots($Adding $3 x$ to both side$)$
$ \Rightarrow 11 x-9 \geq 35$
$ \Rightarrow 11 x-9+9 \geq 35+9 ..($Adding $9$ to both sides$)$
$ \Rightarrow 11 x \geq 44$
$ \Rightarrow \frac{11 x}{11} \geq \frac{44}{11} ...($Dividing both side by $11)$
$ \Rightarrow x \geq 4...($Adding $3 x$ to both sides$)$
$\therefore$ The required graph is:

View full question & answer→

Question 55 Marks

Solve $\frac{2}{3}(x+1)+4<10$ and represent its solution on a number line. Given replacement set is $\{-8,-6,-4,3,6,8,12\}$.

Answer

$\frac{2}{3}(x+1)+4<10$
$\Rightarrow \frac{2}{3}(\mathrm{x}-1)<10-4$
$\Rightarrow \frac{2}{3}(\mathrm{x}-1)<6$
$\Rightarrow 2(x-1)<18$
$\Rightarrow x-1<9$
$\Rightarrow x-1+1<9+1 \ldots ($Adding $1$ to both sides$)$
$\Rightarrow x<10$

Thus $x<10$
Since, replacement set $=\{-8,-6,-4,3,6,8,12\}$
$\Rightarrow$ Solution set $=\{-8,-6,-4,3,6,8\}$

View full question & answer→

Question 65 Marks

Solve and graph the solution set on a number line : $\frac{2}{3} \mathrm{x}+5 \leq \frac{1}{2} \mathrm{x}+6 ; \mathrm{x} \in \mathrm{W}$

Answer

$\frac{2}{3} x+5 \leq \frac{1}{2} x+6$
$\Rightarrow \frac{2}{3} \mathrm{x} \times 6+5 \times 6 \leq \frac{1}{2} \mathrm{x} \times 6+6 \times 6 \ldots ($Multiplying both sides by $6 )$
$\Rightarrow 4 x+30 \leq 3 x+36$
$\Rightarrow 4 x-3 x+30 \leq 3 x-3 x+36 \ldots($ Substracting $3 x$ from both sides$)$
$\Rightarrow x+30 \leq 36$
$\Rightarrow x+30-30 \leq 36-30 \ldots ($Substracting $30$ from both sides$)$
$x \leq 6$
$\therefore$ The required graph is:

View full question & answer→

MATHS [5 marks sum]

Test yourself on this topic