Question5 decreased by the sum of 8 and $n$ . Is $\frac{3 a + 4 b}{2} = -7$ true for $a=6$ and $b=-1$ ? Show your work.

Studdy Solution

STEP 1

Assumptions1. For part c, we are asked to express the phrase "5 decreased by the sum of8 and $n$ " as a mathematical expression. . For part d, we are asked to express the phrase "5 less than8 times a number" as a mathematical expression.
3. For the true or false question, we are given the expression $\frac{3 a+4 b}{}$ and asked to determine if it equals -7 when $a=6$ and $b=-1$ .

STEP 2

For part c, "5 decreased by the sum of8 and $n$ " can be translated into a mathematical expression. "Decreased by" means subtraction and "the sum of8 and $n$ " means $8 + n$ . So, the phrase can be written as $5 - (8 + n)$

STEP 3

For part d, "5 less than8 times a number" can be translated into a mathematical expression. "5 less than" means subtraction and "8 times a number" means $8n$ . So, the phrase can be written as $8n -5$

STEP 4

For the true or false question, we need to substitute $a=6$ and $b=-1$ into the expression $\frac{3 a+4 b}{2}$ and see if it equals -7.
$\frac{3 a+4 b}{2} = \frac{3 \cdot6 +4 \cdot (-1)}{2}$

STEP 5

Calculate the numerator of the fraction.
$3 \cdot +4 \cdot (-1) =18 -4 =14$ So, the expression becomes $\frac{14}{2}$

STEP 6

Calculate the value of the fraction.
$\frac{14}{2} =$

STEP 7

Compare the calculated value with -7. Since7 is not equal to -7, the statement "The expression $\frac{3 a+4 b}{2}$ equals -7 when $a=6$ and $b=-1$ " is false.

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Question5 decreased by the sum of 8 and $n$ . Is $\frac{3 a + 4 b}{2} = -7$ true for $a=6$ and $b=-1$ ? Show your work.

Studdy Solution

STEP 1

STEP 2

For part c, "5 decreased by the sum of8 and $n$ " can be translated into a mathematical expression. "Decreased by" means subtraction and "the sum of8 and $n$ " means $8 + n$ . So, the phrase can be written as $5 - (8 + n)$

STEP 3

For part d, "5 less than8 times a number" can be translated into a mathematical expression. "5 less than" means subtraction and "8 times a number" means $8n$ . So, the phrase can be written as $8n -5$

STEP 4

For the true or false question, we need to substitute $a=6$ and $b=-1$ into the expression $\frac{3 a+4 b}{2}$ and see if it equals -7.
$\frac{3 a+4 b}{2} = \frac{3 \cdot6 +4 \cdot (-1)}{2}$

STEP 5

Calculate the numerator of the fraction.
$3 \cdot +4 \cdot (-1) =18 -4 =14$ So, the expression becomes $\frac{14}{2}$

STEP 6

Calculate the value of the fraction.
$\frac{14}{2} =$

STEP 7

Compare the calculated value with -7. Since7 is not equal to -7, the statement "The expression $\frac{3 a+4 b}{2}$ equals -7 when $a=6$ and $b=-1$ " is false.

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Question5 decreased by the sum of 8 and nnn. Is 3a+4b2=−7\frac{3 a + 4 b}{2} = -723a+4b​=−7 true for a=6a=6a=6 and b=−1b=-1b=−1? Show your work.

Studdy Solution

STEP 1

STEP 2

For part c, "5 decreased by the sum of8 and nnn" can be translated into a mathematical expression. "Decreased by" means subtraction and "the sum of8 and nnn" means 8+n8 + n8+n. So, the phrase can be written as5−(8+n)5 - (8 + n)5−(8+n)

STEP 3

For part d, "5 less than8 times a number" can be translated into a mathematical expression. "5 less than" means subtraction and "8 times a number" means 8n8n8n. So, the phrase can be written as8n−58n -58n−5

STEP 4

For the true or false question, we need to substitute a=6a=6a=6 and b=−1b=-1b=−1 into the expression 3a+4b2\frac{3 a+4 b}{2}23a+4b​ and see if it equals -7.3a+4b2=3⋅6+4⋅(−1)2\frac{3 a+4 b}{2} = \frac{3 \cdot6 +4 \cdot (-1)}{2}23a+4b​=23⋅6+4⋅(−1)​

STEP 5

Calculate the numerator of the fraction.3⋅+4⋅(−1)=18−4=143 \cdot +4 \cdot (-1) =18 -4 =143⋅+4⋅(−1)=18−4=14So, the expression becomes142\frac{14}{2}214​

STEP 6

Calculate the value of the fraction.142=\frac{14}{2} =214​=

STEP 7

Compare the calculated value with -7. Since7 is not equal to -7, the statement "The expression 3a+4b2\frac{3 a+4 b}{2}23a+4b​ equals -7 when a=6a=6a=6 and b=−1b=-1b=−1" is false.

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Question5 decreased by the sum of 8 and $n$ . Is $\frac{3 a + 4 b}{2} = -7$ true for $a=6$ and $b=-1$ ? Show your work.

For part c, "5 decreased by the sum of8 and $n$ " can be translated into a mathematical expression. "Decreased by" means subtraction and "the sum of8 and $n$ " means $8 + n$ . So, the phrase can be written as $5 - (8 + n)$

For part d, "5 less than8 times a number" can be translated into a mathematical expression. "5 less than" means subtraction and "8 times a number" means $8n$ . So, the phrase can be written as $8n -5$

For the true or false question, we need to substitute $a=6$ and $b=-1$ into the expression $\frac{3 a+4 b}{2}$ and see if it equals -7.
$\frac{3 a+4 b}{2} = \frac{3 \cdot6 +4 \cdot (-1)}{2}$

Calculate the numerator of the fraction.
$3 \cdot +4 \cdot (-1) =18 -4 =14$ So, the expression becomes $\frac{14}{2}$

Calculate the value of the fraction.
$\frac{14}{2} =$

Compare the calculated value with -7. Since7 is not equal to -7, the statement "The expression $\frac{3 a+4 b}{2}$ equals -7 when $a=6$ and $b=-1$ " is false.