Inequalities Quiz: Greater Than and Less Than Basics

1) Which of the following inequalities represents "7 is greater than 3"?

7<3

7>3

3>7

3=7

The inequality 7>3 correctly states that 7 is greater than 3. In mathematical terms, the symbol ">" denotes that the number on the left is greater than the number on the right. Hence, 7>3 is the correct representation of the statement "7 is greater than 3".

Explanation

The inequality 7>3 correctly states that 7 is greater than 3. In mathematical terms, the symbol ">" denotes that the number on the left is greater than the number on the right. Hence, 7>3 is the correct representation of the statement "7 is greater than 3".

2) Which inequality symbol correctly completes the statement: −2 _−5?

>

<

≥

≤

Negative numbers can be tricky. On a number line, numbers to the right are greater than those to the left. Therefore, −2 is greater than −5 because it is closer to zero. The correct inequality symbol to complete the statement is >, making it −2>−5.

Explanation

Negative numbers can be tricky. On a number line, numbers to the right are greater than those to the left. Therefore, −2 is greater than −5 because it is closer to zero. The correct inequality symbol to complete the statement is >, making it −2>−5.

3) If x>5 and x<10, which of the following could be a value of x?

4

11

6

10

Given the inequality $x > 5$ and $x < 10$ , the value of $x$ must be greater than 5 and less than 10.

4 is not greater than 5, so it doesn't satisfy $x > 5.$

11 is not less than 10, so it doesn't satisfy $x < 10$ .

10 is not less than 10, so it doesn't satisfy $x < 10$ .

6 is greater than 5 and less than 10, so it satisfies both conditions $x > 5$ and $x < 10$ .

Therefore, the value of x could be 6.

Explanation

Given the inequality $x > 5$ and $x < 10$ , the value of $x$ must be greater than 5 and less than 10.

4 is not greater than 5, so it doesn't satisfy $x > 5.$

11 is not less than 10, so it doesn't satisfy $x < 10$ .

10 is not less than 10, so it doesn't satisfy $x < 10$ .

6 is greater than 5 and less than 10, so it satisfies both conditions $x > 5$ and $x < 10$ .

Therefore, the value of x could be 6.

4) For which values of x is the inequality x²<16 true?

−4<x<4

X>4

X<−4

X≤4

The inequality x²<16 means that the square of xxx must be less than 16. Taking the square root of both sides of the inequality x²<16, we get: ∣x∣<4 This implies that x is between -4 and 4, but does not include -4 and 4 themselves (since x² would be 16 if x were ±4). Therefore, the values of x that satisfy x²<16 are −4<x<4.

Explanation

The inequality x²<16 means that the square of xxx must be less than 16. Taking the square root of both sides of the inequality x²<16, we get: ∣x∣<4 This implies that x is between -4 and 4, but does not include -4 and 4 themselves (since x² would be 16 if x were ±4). Therefore, the values of x that satisfy x²<16 are −4<x<4.

5) Solve the inequality: 2(x−3)>4. What is the range of x?

X>5

X>4

X>3

X>2

To solve the inequality 2(x−3)>4:

First, divide both sides by 2: 2(x-3)/2> 4/2= x−3>2

Next, add 3 to both sides to isolate x: 3+(x-3)>2+3= x>5

Therefore, the range of x that satisfies the inequality 2(x−3)>4 is x>5.

Explanation

To solve the inequality 2(x−3)>4:

First, divide both sides by 2: 2(x-3)/2> 4/2= x−3>2

Next, add 3 to both sides to isolate x: 3+(x-3)>2+3= x>5

Therefore, the range of x that satisfies the inequality 2(x−3)>4 is x>5.

6) If a<b and b<c, which of the following is true?

A>c

A<c

C<a

C=a

If a is less than b and b is less than c, then by the transitive property of inequalities, a must be less than c. This is because aaa being less than b and b being less than c logically means that aaa is also less than c.

Explanation

If a is less than b and b is less than c, then by the transitive property of inequalities, a must be less than c. This is because aaa being less than b and b being less than c logically means that aaa is also less than c.

7) Which value of x satisfies both inequalities: x+2>5 and x−3<1?

X>3

X<4

3<x<4

2<x<3

Solve each inequality separately:

For x+2>5: Subtract 2 from both sides: x+2-2 > 5-2= x>3

For x−3<1: Add 3 to both sides: x-3+3<1+3 = x<4

Combining these results, the values of x that satisfy both inequalities are those that lie between 3 and 4: 3<x<4

Explanation

Solve each inequality separately:

For x+2>5: Subtract 2 from both sides: x+2-2 > 5-2= x>3

For x−3<1: Add 3 to both sides: x-3+3<1+3 = x<4

Combining these results, the values of x that satisfy both inequalities are those that lie between 3 and 4: 3<x<4

8) Solve the inequality: 3y−7<5. What is the range of y?

Y<4

Y<2

Y>4

Y>2

To solve 3y−7<5:

Add 7 to both sides: 3y−7+7<5+7

3y<12

Divide both sides by 3:

3y/3 < 12/3

y<4

Explanation

To solve 3y−7<5:

Add 7 to both sides: 3y−7+7<5+7

3y<12

Divide both sides by 3:

3y/3 < 12/3

y<4

9) Which of the following is true if 5x+3≤18?

X≥3

X≤3

X≥5

X≤5

To solve the inequality 5x+3≤18:

Subtract 3 from both sides: 5x+3−3 ≤ 18−3 = 5x ≤ 15

Next, divide both sides by 5: 5x/5 ≤ 15/5 = x ≤ 3

Therefore, x ≤ 3 is the correct solution.

Explanation

To solve the inequality 5x+3≤18:

Subtract 3 from both sides: 5x+3−3 ≤ 18−3 = 5x ≤ 15

Next, divide both sides by 5: 5x/5 ≤ 15/5 = x ≤ 3

Therefore, x ≤ 3 is the correct solution.

10) Solve the compound inequality: 1<2y+3<7. What is the range of y?

−1<y<2

0<y<2

1<y<3

−2<y<1

Solve the compound inequality in two parts:

Solve 1<2y+3:

Subtract 3 from both sides: 1−3 < 2y+3 - 3 = -2 < 2y

Divide by 2: -2/2 < 2y/2 = -1 < y

Solve 2y+3<7:

Subtract 3 from both sides: 2y+3 -3 < 7-3 = 2y < 4

Divide by 2: 2y/2 < 4/2 = y< 2

Combining these results, we get: −1 < y < 2

Explanation

Solve the compound inequality in two parts:

Solve 1<2y+3:

Subtract 3 from both sides: 1−3 < 2y+3 - 3 = -2 < 2y

Divide by 2: -2/2 < 2y/2 = -1 < y

Solve 2y+3<7:

Subtract 3 from both sides: 2y+3 -3 < 7-3 = 2y < 4

Divide by 2: 2y/2 < 4/2 = y< 2

Combining these results, we get: −1 < y < 2