Question Write expressions for: $6x - 9$ , $\frac{6}{3} \times 8$ , and $x - 12$ .

Studdy Solution

STEP 1

Assumptions
1. "a number" refers to a variable, which we will denote as $x$ .
2. "six times a number less nine" means we multiply the number by six and then subtract nine.
3. "eight times the quotient of 6 and 3" means we first find the quotient of 6 and 3, then multiply the result by eight.
4. "the difference between a number and 12" means we subtract 12 from the number.

STEP 2

For part a, we translate "six times a number less nine" into an algebraic expression. "Six times a number" is $6x$ , and "less nine" means we subtract nine from this product.
$6x - 9$

STEP 3

For part b, we first find the quotient of 6 and 3, which is $\frac{6}{3}$ . Then we multiply this quotient by eight.
$8 \times \left(\frac{6}{3}\right)$

STEP 4

Simplify the quotient inside the parentheses.
$\frac{6}{3} = 2$

STEP 5

Now multiply the simplified quotient by eight.
$8 \times 2$

STEP 6

Calculate the result of the multiplication.
$8 \times 2 = 16$

STEP 7

For part c, we translate "the difference between a number and 12" into an algebraic expression. "The difference" means we subtract, and since it is "between a number and 12", we subtract 12 from the number $x$ .
$x - 12$
The expressions for the given verbal descriptions are: a. $6x - 9$ b. $16$ c. $x - 12$

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Question Write expressions for: $6x - 9$ , $\frac{6}{3} \times 8$ , and $x - 12$ .

Studdy Solution

STEP 1

STEP 2

For part a, we translate "six times a number less nine" into an algebraic expression. "Six times a number" is $6x$ , and "less nine" means we subtract nine from this product.
$6x - 9$

STEP 3

For part b, we first find the quotient of 6 and 3, which is $\frac{6}{3}$ . Then we multiply this quotient by eight.
$8 \times \left(\frac{6}{3}\right)$

STEP 4

Simplify the quotient inside the parentheses.
$\frac{6}{3} = 2$

STEP 5

Now multiply the simplified quotient by eight.
$8 \times 2$

STEP 6

Calculate the result of the multiplication.
$8 \times 2 = 16$

STEP 7

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Question Write expressions for: 6x−96x - 96x−9, 63×8\frac{6}{3} \times 836​×8, and x−12x - 12x−12.

Studdy Solution

STEP 1

STEP 2

For part a, we translate "six times a number less nine" into an algebraic expression. "Six times a number" is 6x 6x 6x, and "less nine" means we subtract nine from this product.6x−96x - 96x−9

STEP 3

For part b, we first find the quotient of 6 and 3, which is 63 \frac{6}{3} 36​. Then we multiply this quotient by eight.8×(63)8 \times \left(\frac{6}{3}\right)8×(36​)

STEP 4

Simplify the quotient inside the parentheses.63=2\frac{6}{3} = 236​=2

STEP 5

Now multiply the simplified quotient by eight.8×28 \times 28×2

STEP 6

Calculate the result of the multiplication.8×2=168 \times 2 = 168×2=16

STEP 7

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Question Write expressions for: $6x - 9$ , $\frac{6}{3} \times 8$ , and $x - 12$ .

For part a, we translate "six times a number less nine" into an algebraic expression. "Six times a number" is $6x$ , and "less nine" means we subtract nine from this product.
$6x - 9$

For part b, we first find the quotient of 6 and 3, which is $\frac{6}{3}$ . Then we multiply this quotient by eight.
$8 \times \left(\frac{6}{3}\right)$

Simplify the quotient inside the parentheses.
$\frac{6}{3} = 2$

Now multiply the simplified quotient by eight.
$8 \times 2$

Calculate the result of the multiplication.
$8 \times 2 = 16$