Question

Solve for $x$ : $3-7x\le -5$

• A. $x\le \frac{5}{7}$
• B. $x\ge \frac{5}{7}$
• C. $x\le -\frac{5}{7}$
• D. $x\ge \frac{5}{7}$

Answer 1

The correct option is A $x\le \frac{5}{7}$

Given algebraic inequality : $3-7x\le -5$

Step 1: Subtract $-3$ from both sides
$\Rightarrow 3-7x-3\le -5-3$
$\Rightarrow -7x\le -8$

Step 2: Divide both sides
of algebraic inequality by $-7$

We know:
If both sides of algebraic inequality are divided or multiplied by a negative number, the sign of inequality is reversed.

$\Rightarrow \frac{-7x}{-7}\ge \frac{-8}{-7}=\frac{8}{7}\Rightarrow x\ge \frac{8}{7}$ ($\because$ same sign on numerator and denominator leads to positive sign of the fraction)
It can be represented in the number line as:
It can be represented on the numberline as:
A closed circle at $\frac{8}{7}$ and the red line goes to the right, indicating that $x$ is greater than or equal to $\frac{8}{7}.$