QuestionDetermine if the following statements are true, false, or open: a. $-4(5 x)=12$ b. $4 \times 6=24$ c. $a+4=6$ , when $a=2$ d. $4 x=19$ , when $x$ equals 5

Studdy Solution

STEP 1

Assumptions
1. We are given four different mathematical statements.
2. We need to determine the truth value of each statement.
3. A statement is "true" if it is correct under the given conditions.
4. A statement is "false" if it is incorrect under the given conditions.
5. A statement is "open" if it cannot be determined to be true or false without additional information.

STEP 2

Evaluate statement a: $-4(5x)=12$ .
We need to determine if this equation is true, false, or open. Since no specific value for $x$ is given, this is an open statement unless it simplifies to an identity or a contradiction.

STEP 3

Simplify the left side of the equation in statement a.
$-4(5x) = -20x$

STEP 4

Compare the simplified form of statement a with the right side of the equation.
Since $-20x$ is not equal to $12$ for all values of $x$ , the statement is not an identity. Without a specific value for $x$ , we cannot determine if the statement is true or false. Thus, statement a is open.

STEP 5

Evaluate statement b: $4 \times 6=24$ .
This is a simple arithmetic operation, and we can calculate the left side to verify if it equals the right side.

STEP 6

Calculate the product on the left side of the equation in statement b.
$4 \times 6 = 24$

STEP 7

Compare the calculated product with the right side of the equation in statement b.
Since $24$ is equal to $24$ , the statement is true.

STEP 8

Evaluate statement c: $a+4=6$ , when $a=2$ .
We are given a specific value for $a$ , so we can substitute this value into the equation to determine if the statement is true or false.

STEP 9

Substitute $a=2$ into the left side of the equation in statement c.
$a+4 = 2+4$

STEP 10

Calculate the sum on the left side of the equation in statement c.
$2+4 = 6$

STEP 11

Compare the calculated sum with the right side of the equation in statement c.
Since $6$ is equal to $6$ , the statement is true.

STEP 12

Evaluate statement d: $4x=19$ , when $x$ equals 5.
We are given a specific value for $x$ , so we can substitute this value into the equation to determine if the statement is true or false.

STEP 13

Substitute $x=5$ into the left side of the equation in statement d.
$4x = 4 \times 5$

STEP 14

Calculate the product on the left side of the equation in statement d.
$4 \times 5 = 20$

STEP 15

Compare the calculated product with the right side of the equation in statement d.
Since $20$ is not equal to $19$ , the statement is false.
Solution:
a. Open b. True c. True d. False

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QuestionDetermine if the following statements are true, false, or open: a. $-4(5 x)=12$ b. $4 \times 6=24$ c. $a+4=6$ , when $a=2$ d. $4 x=19$ , when $x$ equals 5

Studdy Solution

STEP 1

STEP 2

Evaluate statement a: $-4(5x)=12$ .
We need to determine if this equation is true, false, or open. Since no specific value for $x$ is given, this is an open statement unless it simplifies to an identity or a contradiction.

STEP 3

Simplify the left side of the equation in statement a.
$-4(5x) = -20x$

STEP 4

Compare the simplified form of statement a with the right side of the equation.
Since $-20x$ is not equal to $12$ for all values of $x$ , the statement is not an identity. Without a specific value for $x$ , we cannot determine if the statement is true or false. Thus, statement a is open.

STEP 5

Evaluate statement b: $4 \times 6=24$ .
This is a simple arithmetic operation, and we can calculate the left side to verify if it equals the right side.

STEP 6

Calculate the product on the left side of the equation in statement b.
$4 \times 6 = 24$

STEP 7

Compare the calculated product with the right side of the equation in statement b.
Since $24$ is equal to $24$ , the statement is true.

STEP 8

Evaluate statement c: $a+4=6$ , when $a=2$ .
We are given a specific value for $a$ , so we can substitute this value into the equation to determine if the statement is true or false.

STEP 9

Substitute $a=2$ into the left side of the equation in statement c.
$a+4 = 2+4$

STEP 10

Calculate the sum on the left side of the equation in statement c.
$2+4 = 6$

STEP 11

Compare the calculated sum with the right side of the equation in statement c.
Since $6$ is equal to $6$ , the statement is true.

STEP 12

Evaluate statement d: $4x=19$ , when $x$ equals 5.
We are given a specific value for $x$ , so we can substitute this value into the equation to determine if the statement is true or false.

STEP 13

Substitute $x=5$ into the left side of the equation in statement d.
$4x = 4 \times 5$

STEP 14

Calculate the product on the left side of the equation in statement d.
$4 \times 5 = 20$

STEP 15

Compare the calculated product with the right side of the equation in statement d.
Since $20$ is not equal to $19$ , the statement is false.
Solution:
a. Open b. True c. True d. False

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QuestionDetermine if the following statements are true, false, or open: a. −4(5x)=12-4(5 x)=12−4(5x)=12 b. 4×6=244 \times 6=244×6=24 c. a+4=6a+4=6a+4=6, when a=2a=2a=2 d. 4x=194 x=194x=19, when xxx equals 5

Studdy Solution

STEP 1

STEP 2

Evaluate statement a: −4(5x)=12-4(5x)=12−4(5x)=12.We need to determine if this equation is true, false, or open. Since no specific value for xxx is given, this is an open statement unless it simplifies to an identity or a contradiction.

STEP 3

Simplify the left side of the equation in statement a.−4(5x)=−20x-4(5x) = -20x−4(5x)=−20x

STEP 4

Compare the simplified form of statement a with the right side of the equation.Since −20x-20x−20x is not equal to 121212 for all values of xxx, the statement is not an identity. Without a specific value for xxx, we cannot determine if the statement is true or false. Thus, statement a is open.

STEP 5

Evaluate statement b: 4×6=244 \times 6=244×6=24.This is a simple arithmetic operation, and we can calculate the left side to verify if it equals the right side.

STEP 6

Calculate the product on the left side of the equation in statement b.4×6=244 \times 6 = 244×6=24

STEP 7

Compare the calculated product with the right side of the equation in statement b.Since 242424 is equal to 242424, the statement is true.

STEP 8

Evaluate statement c: a+4=6a+4=6a+4=6, when a=2a=2a=2.We are given a specific value for aaa, so we can substitute this value into the equation to determine if the statement is true or false.

STEP 9

Substitute a=2a=2a=2 into the left side of the equation in statement c.a+4=2+4a+4 = 2+4a+4=2+4

STEP 10

Calculate the sum on the left side of the equation in statement c.2+4=62+4 = 62+4=6

STEP 11

Compare the calculated sum with the right side of the equation in statement c.Since 666 is equal to 666, the statement is true.

STEP 12

Evaluate statement d: 4x=194x=194x=19, when xxx equals 5.We are given a specific value for xxx, so we can substitute this value into the equation to determine if the statement is true or false.

STEP 13

Substitute x=5x=5x=5 into the left side of the equation in statement d.4x=4×54x = 4 \times 54x=4×5

STEP 14

Calculate the product on the left side of the equation in statement d.4×5=204 \times 5 = 204×5=20

STEP 15

Compare the calculated product with the right side of the equation in statement d.Since 202020 is not equal to 191919, the statement is false.Solution:a. Open b. True c. True d. False

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QuestionDetermine if the following statements are true, false, or open: a. $-4(5 x)=12$ b. $4 \times 6=24$ c. $a+4=6$ , when $a=2$ d. $4 x=19$ , when $x$ equals 5

Evaluate statement a: $-4(5x)=12$ .
We need to determine if this equation is true, false, or open. Since no specific value for $x$ is given, this is an open statement unless it simplifies to an identity or a contradiction.

Simplify the left side of the equation in statement a.
$-4(5x) = -20x$

Compare the simplified form of statement a with the right side of the equation.
Since $-20x$ is not equal to $12$ for all values of $x$ , the statement is not an identity. Without a specific value for $x$ , we cannot determine if the statement is true or false. Thus, statement a is open.

Evaluate statement b: $4 \times 6=24$ .
This is a simple arithmetic operation, and we can calculate the left side to verify if it equals the right side.

Calculate the product on the left side of the equation in statement b.
$4 \times 6 = 24$

Compare the calculated product with the right side of the equation in statement b.
Since $24$ is equal to $24$ , the statement is true.

Evaluate statement c: $a+4=6$ , when $a=2$ .
We are given a specific value for $a$ , so we can substitute this value into the equation to determine if the statement is true or false.

Substitute $a=2$ into the left side of the equation in statement c.
$a+4 = 2+4$

Calculate the sum on the left side of the equation in statement c.
$2+4 = 6$

Compare the calculated sum with the right side of the equation in statement c.
Since $6$ is equal to $6$ , the statement is true.

Evaluate statement d: $4x=19$ , when $x$ equals 5.
We are given a specific value for $x$ , so we can substitute this value into the equation to determine if the statement is true or false.

Substitute $x=5$ into the left side of the equation in statement d.
$4x = 4 \times 5$

Calculate the product on the left side of the equation in statement d.
$4 \times 5 = 20$

Compare the calculated product with the right side of the equation in statement d.
Since $20$ is not equal to $19$ , the statement is false.
Solution:
a. Open b. True c. True d. False