Question

The solution of the inequality $\frac{1-x}{2}<4$ is:

• A. $x<-7$
• B. $x>-7$
• C. $x>7$
• D. $x<7$

Answer 1

The correct option is B $x>-7$

Given, $\frac{1-x}{2}<4$

Step 1: Multiply both sides of the equation by 2 to eliminate 2 on the left side of the equation.
Also, multiplying both sides of the inequality by a positive number does not change the direction of the inequality.
$\frac{1-x}{2}\times 2<4\times 2$
$\Rightarrow 1-x<8$

Step 2: Subtract both sides of the equation by 1 to eliminate 1 on the left side of the equation.
Also, subtracting both sides of the inequality by a positive number does not change the direction of the inequality.
$1-x-1<8-1$
$-x<7$

Step 3: Divide both sides of the equation by -1.
Also, dividing both sides of the inequality by a negative number changes the direction of the inequality.
$\frac{-x}{-1}>\frac{7}{-1}$
$x>-7$

Hence, solution of the inequality $\frac{1-x}{2}<4$ is $x>-7.$