Question

Find the value of unknown in the algebraic inequality $4(9x+1)\ge 9$

• A. $x>\frac{5}{36}$
• B. $x\le \frac{5}{36}$
• C. $x\ge \frac{5}{36}$
• D. $x<-\frac{5}{36}$

Answer 1

The correct option is C $x\ge \frac{5}{36}$

Given algebraic inequality : $4(9x+1)\ge 9$

Step 1: Divide by 4 on both the sides of the inequality
$\Rightarrow \frac{4(9x+1)}{4}\ge \frac{9}{4}$
$\Rightarrow 9x+1\ge \frac{9}{4}$

Step 2: Subtract 1 on both sides of the inequality
$\Rightarrow 9x+1-1\ge \frac{9}{4}-1$
$\Rightarrow 9x\ge \frac{9}{4}-\frac{4}{4}(\because \frac{4}{4}=1)\Rightarrow 9x\ge \frac{5}{4}$
$\Rightarrow 9x\ge \frac{5}{4}$

Step 3: Divide by 9 on both sides of the inequality
$\Rightarrow \frac{9x}{9}\ge \frac{5}{4\times 9}$

$\Rightarrow x\ge \frac{5}{36}$
It can be represented on the numberline as:
A closed circle at $\frac{5}{36}$ and the red line goes to the right, indicating that $x$ is greater than or equal to $\frac{5}{36}$