Solving Inequalities using the Operations of Addition and Subtraction

Q.

Write an inequality that can be solved using the Subtraction Property of Inequality and has a solution of all numbers less than $-3$.

Q. Two numbers are in the ratio $2:3$ and their sum is less than $15$. Select the pair satisfying the above conditions.

1. $4,6$
2. $5,10$
3. $1,2$
4. $6,9$

Q. The inequality holds true when a number or unknown is added to or subtracted from both sides.

1. True
2. False

Q. If $4x\le -3$, then $4x\times (-3)$$(-3)\times (-3)$.
If $-3x>4$, then $(-3x)\times \left(4\right)$$4\times 4$.

1. $<$
2. $>$
3. $\le$
4. $\ge$

Q. Which one of the following inequalities is represented on this number line?

1. $x+7>5$
2. $x-10<-14$
3. $x+3<1$
4. $x-15\le -17$

Q. If two algebraic inequalities for the same unknown integer $x$ are $x+2>9\&x-3<7$, then what are the possible values of $x$.

1. $7,8,9\&10$
2. $8\&9$
3. $9{\&}^{}10$

Q. Solve for $x$: $x+20\le 50$

1. $x\le 30$
2. $x\le 20$
3. $x\le -30$

Q.

Tell whether the given value is a solution of the inequality.

$n–3\le 4;n=7$

Q. If $x\ge 2$, then $x-2\ge$

1. $8$
2. $-4$
3. $0$

Q. Which of the following option(s) satisfy the inequality $x-3\le 12?$

1. $x=16$
2. $x=15$
3. $x=10$
4. $x=20$

Q. Represent the inequality $x+7\ge 7$ on the number line.

Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

1. 
2. 
3. 
4. 

Q. Match the inequalities with a possible solutions of $i$. Here, $i$ is an integer.

1. $0$
2. $-2$
3. $-5$
4. $10$

Q. What number should be placed in the yellow diamond?​

Q. If $a\ge b$, then $a+c\ge b+c$ where $a,b\&c$ are integers.

1. False
2. True

Q. Solution of the inequality $x+5>15,$ is:

1. $x<10$
2. $x=10$
3. $x>15$
4. $x>10$

Q. If $x-3\le 3$, the the value of the unknown is

1. $\le 6$
2. $\ge 6$
3. $\le 0$