Question

(a) If $x<5,$ then $x-3\_\_\_\_\_\_\_\_\_\_2$.

(b) If $x\le 5,$ then $3x\_\_\_\_\_\_\_\_\_\_15$.

(c) If $x\ge 2,$ then $-3x\_\_\_\_\_\_\_\_\_\_-6$

(d)If $x<-2,$ then $-x\_\_\_\_\_\_\_\_\_\_2$.

Short answer

(a) The required answer is$x-3>2$.

(b)The required answer is $3x\le 15$.

(c)The required answer is $-3x\le -6$.

(d) The required answer is $-x\le 2$.

Step-by-step solution

Part a. Step 1. Assumption of the variable.

Since, we have to fill the given blank with an appropriate inequality sign.

Let $x<5$.

Part a. Step 2. Apply the operation subtraction.

$x-3<5-3$

$x-3<2$.

Part a. Step 3. Decision of inequality.

Therefore, if$x<5$then, $x-3<2$.

Part b. Step 1. Assumption of the variable.

Since, we have to fill the given blank with an appropriate inequality sign.

Let $x\le 5$.

Part b. Step 2. Apply the operation multiplication.

$\begin{array}{c}3x\le 5\\ 3x\le 3\left(5\right)\\ 3x\le 15.\end{array}$

Part b. Step 3. Decision of inequality.

Therefore, if $x\le 5$then, $3x\le 15$

Part c. Step 1. Assumption of the variable.

Since, we have to fill the given blank with an appropriate inequality sign.

Let $x\ge 2$.

Part c. Step 2. Apply the operation multiplication.

$x\ge 2$

$-3x<-6$. (Multiply$-3$ both sides).

Part c. Step 3. Decision of inequality.

Therefore, if$x\ge 2$then, $-3x\le -6$.

Part d. Step 1. Assumption of the variable.

Since, we have to fill the given blank with an appropriate inequality sign.

Let $x<-2$.

Part d. Step 2. Apply the operation multiplication.

$x<-2$

$-x>2$. (Multiply$-1$ both sides).

Part d. Step 3. Decision of inequality.

Therefore, if $x<-2$then, $-x>2$