Question

Find $y$ in the algebraic inequality $99(4y-7)\le \frac{3}{4}-\frac{1}{2}$

• A. $y\le \frac{2773}{1584}$
• B. $y\ge \frac{2773}{1584}$
• C. $y\le \frac{1584}{2773}$
• D. $y\ge \frac{1584}{2773}$

Answer 1

The correct option is A $y\le \frac{2773}{1584}$

Given algebraic inequality : $99(4y-7)\le \frac{3}{4}-\frac{1}{2}$
Simplify the R.H.S:
$\Rightarrow 99(4y-7)\le \frac{3}{4}-\frac{1\times 2}{2\times 2}(\because \text{Making the denominators the same})$
$\Rightarrow 99(4y-7)\le \frac{3}{4}-\frac{2}{4}$
$\Rightarrow 99(4y-7)\le \frac{3-2}{4}\Rightarrow 99(4y-7)\le \frac{1}{4}$

Step 1: Multiply 99 inside the bracket
$\Rightarrow 99\times 4y-99\times 7\le \frac{1}{4}$
$\Rightarrow 396y-693\le \frac{1}{4}$

Step 2: Add 693 to both sides of the inequality
$\Rightarrow 396y+693-693\le \frac{1}{4}+693$
$\Rightarrow 396y\le \frac{1+2772}{4}$

$\Rightarrow 396y\le \frac{2773}{4}$


Step 3: Divide by 396 on both the sides
$\Rightarrow \frac{396y}{396}\le \frac{2773}{4\times 396}$

$\Rightarrow y\le \frac{2773}{1584}$

It can be represented on the numberline as:
A closed circle at $\frac{2773}{1584}$ and the red line goes to the left, indicating that $y$ is less than or equal to $\frac{2773}{1584}.$