Math / Algebra

QuestionWrite an equivalent expression. $\frac{1}{3}(12 x+6 x-21)=\square x-\square$

Studdy Solution

STEP 1

1. The expression $\frac{1}{3}(12x + 6x - 21)$ needs to be simplified and rewritten in the form $\square x - \square$ .
2. The expression inside the parentheses can be simplified by combining like terms.
3. Distributive property will be used to eliminate the fraction.

STEP 2

1. Simplify the expression inside the parentheses by combining like terms.
2. Apply the distributive property to eliminate the fraction.
3. Rewrite the expression in the form $\square x - \square$ .

STEP 3

Combine like terms inside the parentheses:
$12x + 6x - 21 = 18x - 21$

STEP 4

Apply the distributive property to eliminate the fraction:
$\frac{1}{3}(18x - 21) = \frac{1}{3} \times 18x - \frac{1}{3} \times 21$

STEP 5

Calculate each term separately:
$\frac{1}{3} \times 18x = 6x$ $\frac{1}{3} \times 21 = 7$

STEP 6

Rewrite the expression in the form $\square x - \square$ :
$6x - 7$
Thus, the equivalent expression is:
$\boxed{6x - 7}$

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QuestionWrite an equivalent expression. $\frac{1}{3}(12 x+6 x-21)=\square x-\square$

Studdy Solution

STEP 1

1. The expression $\frac{1}{3}(12x + 6x - 21)$ needs to be simplified and rewritten in the form $\square x - \square$ .
2. The expression inside the parentheses can be simplified by combining like terms.
3. Distributive property will be used to eliminate the fraction.

STEP 2

1. Simplify the expression inside the parentheses by combining like terms.
2. Apply the distributive property to eliminate the fraction.
3. Rewrite the expression in the form $\square x - \square$ .

STEP 3

Combine like terms inside the parentheses:
$12x + 6x - 21 = 18x - 21$

STEP 4

Apply the distributive property to eliminate the fraction:
$\frac{1}{3}(18x - 21) = \frac{1}{3} \times 18x - \frac{1}{3} \times 21$

STEP 5

Calculate each term separately:
$\frac{1}{3} \times 18x = 6x$ $\frac{1}{3} \times 21 = 7$

STEP 6

Rewrite the expression in the form $\square x - \square$ :
$6x - 7$
Thus, the equivalent expression is:
$\boxed{6x - 7}$

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QuestionWrite an equivalent expression. 13(12x+6x−21)=□x−□\frac{1}{3}(12 x+6 x-21)=\square x-\square31​(12x+6x−21)=□x−□

Studdy Solution

STEP 1

STEP 2

1. Simplify the expression inside the parentheses by combining like terms.2. Apply the distributive property to eliminate the fraction.3. Rewrite the expression in the form □x−□\square x - \square□x−□.

STEP 3

Combine like terms inside the parentheses:12x+6x−21=18x−21 12x + 6x - 21 = 18x - 21 12x+6x−21=18x−21

STEP 4

Apply the distributive property to eliminate the fraction:13(18x−21)=13×18x−13×21 \frac{1}{3}(18x - 21) = \frac{1}{3} \times 18x - \frac{1}{3} \times 21 31​(18x−21)=31​×18x−31​×21

STEP 5

Calculate each term separately:13×18x=6x \frac{1}{3} \times 18x = 6x 31​×18x=6x 13×21=7 \frac{1}{3} \times 21 = 7 31​×21=7

STEP 6

Rewrite the expression in the form □x−□\square x - \square□x−□:6x−7 6x - 7 6x−7Thus, the equivalent expression is:6x−7 \boxed{6x - 7} 6x−7​

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QuestionWrite an equivalent expression. $\frac{1}{3}(12 x+6 x-21)=\square x-\square$

1. Simplify the expression inside the parentheses by combining like terms.
2. Apply the distributive property to eliminate the fraction.
3. Rewrite the expression in the form $\square x - \square$ .

Combine like terms inside the parentheses:
$12x + 6x - 21 = 18x - 21$

Apply the distributive property to eliminate the fraction:
$\frac{1}{3}(18x - 21) = \frac{1}{3} \times 18x - \frac{1}{3} \times 21$

Calculate each term separately:
$\frac{1}{3} \times 18x = 6x$ $\frac{1}{3} \times 21 = 7$

Rewrite the expression in the form $\square x - \square$ :
$6x - 7$
Thus, the equivalent expression is:
$\boxed{6x - 7}$