Question

a) Solve the following inequation: $-2\frac{3}{4}\le x+\frac{1}{4}<4\frac{1}{4},xϵR$

b) Solve the following inequation:$\frac{2x+1}{2}+2(3-x)\ge 7,xϵR$

[6 MARKS]

Answer 1

Each subpart: 3 Marks

a) $-2\frac{3}{4}\le x+\frac{1}{4}<4\frac{1}{4},xϵR\Rightarrow -\frac{11}{4}\le \frac{4x+1}{4}<\frac{17}{4}$
Multiplying all sides by 4, we get
$\Rightarrow -11\le 4x+1<17\Rightarrow -11-1\le 4x<17-1\Rightarrow -12\le 4x<16\Rightarrow -3\le x<4,xϵR$

b) $\frac{2x+1}{2}+2(3-x)\ge 7,xϵR\Rightarrow \frac{2x+1+12-4x}{2}\ge 7\Rightarrow -2x+13\ge 14\Rightarrow -2x\ge 14-13\Rightarrow -2x\ge 1\Rightarrow x\le -\frac{1}{2},xϵR$