Question

Is(4, 3)a solution to the inequality 3x + y ≥ 20?

Yes or no

Answer 1

To determine if (4, 3) is a solution to the inequality \(3x + y \geq 20\), we can substitute \(x = 4\) and \(y = 3\) into the inequality:

\[
3(4) + 3 \geq 20
\]

Calculating the left side:

\[
12 + 3 = 15
\]

Now we check the inequality:

\[
15 \geq 20
\]

This statement is false. Therefore, the point (4, 3) is not a solution to the inequality \(3x + y \geq 20\).

So, the answer is **no**.

Answer 2

Doesthepoint(1, 10) satisfy the inequality y < 7x + 1?

yes or no

Answer 3

To determine if the point (1, 10) satisfies the inequality \( y < 7x + 1 \), we can substitute \( x = 1 \) and see if \( y \) is less than \( 7 \cdot 1 + 1 \).

First, calculate the right side:

\[
7(1) + 1 = 7 + 1 = 8
\]

Now, we check the inequality:

\[
10 < 8
\]

This statement is false. Therefore, the point (1, 10) does not satisfy the inequality \( y < 7x + 1 \).

So, the answer is **no**.

Answer 4

Does(2, 3)maketheinequality2x + 3y < 20true?

Answer 5

To determine if the point (2, 3) satisfies the inequality \(2x + 3y < 20\), we can substitute \(x = 2\) and \(y = 3\) into the inequality.

Calculating the left side:

\[
2(2) + 3(3) < 20
\]

Now, compute the values:

\[
4 + 9 < 20
\]

This simplifies to:

\[
13 < 20
\]

This statement is true. Therefore, the point (2, 3) does satisfy the inequality \(2x + 3y < 20\).

So, the answer is **yes**.

Answer 6

Is(4, 9)asolutiontotheinequalityy ≤ 2x + 1?

Answer 7

To determine if the point (4, 9) satisfies the inequality \(y \leq 2x + 1\), we can substitute \(x = 4\) and \(y = 9\) into the inequality.

First, calculate the right side:

\[
2(4) + 1 = 8 + 1 = 9
\]

Now, we check the inequality:

\[
9 \leq 9
\]

This statement is true. Therefore, the point (4, 9) is a solution to the inequality \(y \leq 2x + 1\).

So, the answer is **yes**.

Answer 8

Doesthepoint(2, 5)satisfytheinequality14x + 20y ≥ 6?

Answer 9

To determine if the point (2, 5) satisfies the inequality \(14x + 20y \geq 6\), we can substitute \(x = 2\) and \(y = 5\) into the inequality.

Calculating the left side:

\[
14(2) + 20(5) \geq 6
\]

Now, compute the values:

\[
28 + 100 \geq 6
\]

This simplifies to:

\[
128 \geq 6
\]

This statement is true. Therefore, the point (2, 5) does satisfy the inequality \(14x + 20y \geq 6\).

So, the answer is **yes**.

Answer 10

Does(1, 7)maketheinequalityy < 7x + 10true?

Answer 11

To determine if the point (1, 7) satisfies the inequality \(y < 7x + 10\), we can substitute \(x = 1\) and \(y = 7\) into the inequality.

First, calculate the right side using \(x = 1\):

\[
7(1) + 10 = 7 + 10 = 17
\]

Now we check the inequality:

\[
7 < 17
\]

This statement is true. Therefore, the point (1, 7) does satisfy the inequality \(y < 7x + 10\).

So, the answer is **yes**.

Answer 12

Doesthepoint(1, 1)satisfytheinequality2x + 12y > 16?

Answer 13

To determine if the point (1, 1) satisfies the inequality \(2x + 12y > 16\), we can substitute \(x = 1\) and \(y = 1\) into the inequality.

Calculating the left side:

\[
2(1) + 12(1) > 16
\]

Now, compute the values:

\[
2 + 12 > 16
\]

This simplifies to:

\[
14 > 16
\]

This statement is false. Therefore, the point (1, 1) does **not** satisfy the inequality \(2x + 12y > 16\).

So, the answer is **no**.

Answer 14

Is(4, 5)asolutiontotheinequalityy ≥ 7x + 3?

Answer 15

To determine if the point (4, 5) satisfies the inequality \(y \geq 7x + 3\), we can substitute \(x = 4\) and \(y = 5\) into the inequality.

First, calculate the right side:

\[
7(4) + 3 = 28 + 3 = 31
\]

Now we check the inequality:

\[
5 \geq 31
\]

This statement is false. Therefore, the point (4, 5) is **not** a solution to the inequality \(y \geq 7x + 3\).

So, the answer is **no**.

Answer 16

Does(1, 10)maketheinequalityy > 6x + 1true?

Answer 17

To determine if the point (1, 10) satisfies the inequality \(y > 6x + 1\), we will substitute \(x = 1\) and \(y = 10\) into the inequality.

First, calculate the right side:

\[
6(1) + 1 = 6 + 1 = 7
\]

Now, check if the inequality holds:

\[
10 > 7
\]

This statement is true. Therefore, the point (1, 10) does satisfy the inequality \(y > 6x + 1\).

So, the answer is **yes**.

Answer 18

Is(–7, 7)asolutiontotheinequality
y
≥
1
7
x
+ 8
?

Answer 19

To determine if the point \((-7, 7)\) satisfies the inequality

\[
y \geq \frac{1}{7}x + 8,
\]

we can substitute \(x = -7\) and \(y = 7\) into the inequality.

First, calculate the right side:

\[
\frac{1}{7}(-7) + 8 = -1 + 8 = 7.
\]

Now we check the inequality:

\[
7 \geq 7.
\]

This statement is true. Therefore, the point \((-7, 7)\) is a solution to the inequality

\[
y \geq \frac{1}{7}x + 8.
\]

So, the answer is **yes**.

Answer 20

Doesthepoint(5, 3)satisfytheinequality2x + 3y > 13?

Answer 21

To determine if the point (5, 3) satisfies the inequality \(2x + 3y > 13\), we can substitute \(x = 5\) and \(y = 3\) into the inequality.

Calculating the left side:

\[
2(5) + 3(3) > 13
\]

Now, compute the values:

\[
10 + 9 > 13
\]

This simplifies to:

\[
19 > 13.
\]

This statement is true. Therefore, the point (5, 3) does satisfy the inequality \(2x + 3y > 13\).

So, the answer is **yes**.

Answer 22

Does(–5, –8)maketheinequalityy < 10true?

Answer 23

To determine if the point \((-5, -8)\) satisfies the inequality \(y < 10\), we can substitute \(y = -8\) into the inequality.

Check the inequality:

\[
-8 < 10.
\]

This statement is true. Therefore, the point \((-5, -8)\) does satisfy the inequality \(y < 10\).

So, the answer is **yes**.

Answer 24

Doesthepoint(–1, 3)satisfytheinequality6x + 6y > 12?

Answer 25

To determine if the point \((-1, 3)\) satisfies the inequality \(6x + 6y > 12\), we can substitute \(x = -1\) and \(y = 3\) into the inequality.

Calculating the left side:

\[
6(-1) + 6(3) > 12
\]

Now, compute the values:

\[
-6 + 18 > 12
\]

This simplifies to:

\[
12 > 12.
\]

This statement is **false** since \(12\) is not greater than \(12\). Therefore, the point \((-1, 3)\) does **not** satisfy the inequality \(6x + 6y > 12\).

So, the answer is **no**.

Answer 26

Is(5, 1)asolutiontotheinequalityy < 10x + 1?

Answer 27

To determine if the point \((5, 1)\) satisfies the inequality \(y < 10x + 1\), we can substitute \(x = 5\) and \(y = 1\) into the inequality.

First, calculate the right side:

\[
10(5) + 1 = 50 + 1 = 51.
\]

Now we check the inequality:

\[
1 < 51.
\]

This statement is **true**. Therefore, the point \((5, 1)\) does satisfy the inequality \(y < 10x + 1\).

So, the answer is **yes**.

Answer 28

Doesthepoint(10, –8)satisfytheinequality5x + 6y ≤ 2?

Answer 29

To determine if the point \((10, -8)\) satisfies the inequality \(5x + 6y \leq 2\), we can substitute \(x = 10\) and \(y = -8\) into the inequality.

Calculating the left side:

\[
5(10) + 6(-8) \leq 2
\]

Now, compute the values:

\[
50 - 48 \leq 2
\]

This simplifies to:

\[
2 \leq 2.
\]

The statement is **true** since \(2\) is equal to \(2\). Therefore, the point \((10, -8)\) does satisfy the inequality \(5x + 6y \leq 2\).

So, the answer is **yes**.

Answer 30

Does(1, 7)maketheinequalityy ≥ 5x + 2true?

Answer 31

To determine if the point \((1, 7)\) satisfies the inequality \(y \geq 5x + 2\), we can substitute \(x = 1\) and \(y = 7\) into the inequality.

First, calculate the right side:

\[
5(1) + 2 = 5 + 2 = 7.
\]

Now we check the inequality:

\[
7 \geq 7.
\]

This statement is **true**. Therefore, the point \((1, 7)\) does satisfy the inequality \(y \geq 5x + 2\).

So, the answer is **yes**.

Answer 32

s(1, 2)asolutiontotheinequality2x + 7y < 18?

Answer 33

To determine if the point \((1, 2)\) satisfies the inequality \(2x + 7y < 18\), we can substitute \(x = 1\) and \(y = 2\) into the inequality.

Calculating the left side:

\[
2(1) + 7(2) < 18
\]

Now compute the values:

\[
2 + 14 < 18
\]

This simplifies to:

\[
16 < 18.
\]

This statement is **true**. Therefore, the point \((1, 2)\) does satisfy the inequality \(2x + 7y < 18\).

So, the answer is **yes**.

Answer 34

Does(8, –2)maketheinequalityx > –2true?

Answer 35

To determine if the point \((8, -2)\) satisfies the inequality \(x > -2\), we can simply check the value of \(x\).

Here, \(x = 8\).

Now, check the inequality:

\[
8 > -2.
\]

This statement is **true**. Therefore, the point \((8, -2)\) does satisfy the inequality \(x > -2\).

So, the answer is **yes**.

Answer 36

Doesthepoint(–2, –5)satisfytheinequality
y
≥
1
2
x
− 4
?

Answer 37

To determine if the point \((-2, -5)\) satisfies the inequality

\[
y \geq \frac{1}{2}x - 4,
\]

we will substitute \(x = -2\) and \(y = -5\) into the inequality.

First, calculate the right side:

\[
\frac{1}{2}(-2) - 4 = -1 - 4 = -5.
\]

Now we check the inequality:

\[
-5 \geq -5.
\]

This statement is **true** since \(-5\) is equal to \(-5\). Therefore, the point \((-2, -5)\) does satisfy the inequality

\[
y \geq \frac{1}{2}x - 4.
\]

So, the answer is **yes**.

Answer 38

Is(–4, 2)asolutiontotheinequalityy > 4x + 10?

Answer 39

To determine if the point \((-4, 2)\) satisfies the inequality

\[
y > 4x + 10,
\]

we can substitute \(x = -4\) and \(y = 2\) into the inequality.

First, calculate the right side:

\[
4(-4) + 10 = -16 + 10 = -6.
\]

Now we check the inequality:

\[
2 > -6.
\]

This statement is **true**. Therefore, the point \((-4, 2)\) does satisfy the inequality

\[
y > 4x + 10.
\]

So, the answer is **yes**.

Answer 40

Does(–2, –5)maketheinequality2x − 20y ≥ –5true?

Answer 41

To determine if the point \((-2, -5)\) satisfies the inequality

\[
2x - 20y \geq -5,
\]

we can substitute \(x = -2\) and \(y = -5\) into the inequality.

Calculating the left side:

\[
2(-2) - 20(-5) \geq -5.
\]

Now compute the values:

\[
-4 + 100 \geq -5.
\]

This simplifies to:

\[
96 \geq -5.
\]

This statement is **true**. Therefore, the point \((-2, -5)\) does satisfy the inequality

\[
2x - 20y \geq -5.
\]

So, the answer is **yes**.

Answer 42

Doesthepoint(10, 10)satisfytheinequality20x − 17y ≥ –12?

Answer 43

To determine if the point \((10, 10)\) satisfies the inequality

\[
20x - 17y \geq -12,
\]

we can substitute \(x = 10\) and \(y = 10\) into the inequality.

Calculating the left side:

\[
20(10) - 17(10) \geq -12.
\]

Now compute the values:

\[
200 - 170 \geq -12.
\]

This simplifies to:

\[
30 \geq -12.
\]

This statement is **true**. Therefore, the point \((10, 10)\) does satisfy the inequality

\[
20x - 17y \geq -12.
\]

So, the answer is **yes**.

Answer 44

Does(–5, –8)maketheinequalityy < –4true?

Answer 45

To determine if the point \((-5, -8)\) satisfies the inequality

\[
y < -4,
\]

we can simply check the value of \(y\).

Here, \(y = -8\).

Now, check the inequality:

\[
-8 < -4.
\]

This statement is **true**. Therefore, the point \((-5, -8)\) does satisfy the inequality \(y < -4\).

So, the answer is **yes**.

Answer 46

Doesthepoint(2, –2)satisfytheinequalityy ≤ 3x − 8?

Answer 47

To determine if the point \((2, -2)\) satisfies the inequality

\[
y \leq 3x - 8,
\]

we can substitute \(x = 2\) and \(y = -2\) into the inequality.

First, calculate the right side:

\[
3(2) - 8 = 6 - 8 = -2.
\]

Now we check the inequality:

\[
-2 \leq -2.
\]

This statement is **true** since \(-2\) is equal to \(-2\). Therefore, the point \((2, -2)\) does satisfy the inequality

\[
y \leq 3x - 8.
\]

So, the answer is **yes**.