Math / Algebra

Question2. Simplify the expression. $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$ $\frac{11}{3} w-15$ $\frac{11}{3} w-5$ $4 w-5$ $4 w-15$

Studdy Solution

STEP 1

1. The given expression is: $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$
2. The goal is to simplify this expression to match one of the given options.
3. Simplification involves distributing, combining like terms, and reducing the expression properly.

STEP 2

1. Distribute the $-5$ through the term $\left(2-\frac{w}{3}\right)$ .
2. Combine like terms involving $w$ .
3. Combine the constant terms.
4. Verify the final simplified expression against the given options.

STEP 3

Distribute $-5$ through $\left(2-\frac{w}{3}\right)$ :
$-5 \left(2 - \frac{w}{3}\right) = -5 \cdot 2 + (-5) \cdot \left(-\frac{w}{3}\right)$
$= -10 + \frac{5w}{3}$

STEP 4

Rewrite the original expression with the distributed terms:
$-10 + \frac{5w}{3} + \frac{7}{3} w - 5$ Combine like terms involving $w$ :
$\frac{5w}{3} + \frac{7w}{3} = \frac{5w + 7w}{3} = \frac{12w}{3} = 4w$

STEP 5

Combine the constant terms:
$-10 - 5 = -15$

STEP 6

Combine the results from the previous steps:
$4w - 15$
Verify against the given options:
$4w - 15$
The simplified expression matches the option $4w - 15$ .
$\boxed{4w - 15}$

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Question2. Simplify the expression. $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$ $\frac{11}{3} w-15$ $\frac{11}{3} w-5$ $4 w-5$ $4 w-15$

Studdy Solution

STEP 1

1. The given expression is: $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$
2. The goal is to simplify this expression to match one of the given options.
3. Simplification involves distributing, combining like terms, and reducing the expression properly.

STEP 2

1. Distribute the $-5$ through the term $\left(2-\frac{w}{3}\right)$ .
2. Combine like terms involving $w$ .
3. Combine the constant terms.
4. Verify the final simplified expression against the given options.

STEP 3

Distribute $-5$ through $\left(2-\frac{w}{3}\right)$ :
$-5 \left(2 - \frac{w}{3}\right) = -5 \cdot 2 + (-5) \cdot \left(-\frac{w}{3}\right)$
$= -10 + \frac{5w}{3}$

STEP 4

Rewrite the original expression with the distributed terms:
$-10 + \frac{5w}{3} + \frac{7}{3} w - 5$ Combine like terms involving $w$ :
$\frac{5w}{3} + \frac{7w}{3} = \frac{5w + 7w}{3} = \frac{12w}{3} = 4w$

STEP 5

Combine the constant terms:
$-10 - 5 = -15$

STEP 6

Combine the results from the previous steps:
$4w - 15$
Verify against the given options:
$4w - 15$
The simplified expression matches the option $4w - 15$ .
$\boxed{4w - 15}$

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Question2. Simplify the expression. −5(2−w3)+73w−5-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5−5(2−3w​)+37​w−5 113w−15\frac{11}{3} w-15311​w−15 113w−5\frac{11}{3} w-5311​w−5 4w−54 w-54w−5 4w−154 w-154w−15

Studdy Solution

STEP 1

1. The given expression is: −5(2−w3)+73w−5-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5−5(2−3w​)+37​w−52. The goal is to simplify this expression to match one of the given options.3. Simplification involves distributing, combining like terms, and reducing the expression properly.

STEP 2

1. Distribute the −5-5−5 through the term (2−w3)\left(2-\frac{w}{3}\right)(2−3w​).2. Combine like terms involving www.3. Combine the constant terms.4. Verify the final simplified expression against the given options.

STEP 3

Distribute −5-5−5 through (2−w3)\left(2-\frac{w}{3}\right)(2−3w​):−5(2−w3)=−5⋅2+(−5)⋅(−w3)-5 \left(2 - \frac{w}{3}\right) = -5 \cdot 2 + (-5) \cdot \left(-\frac{w}{3}\right)−5(2−3w​)=−5⋅2+(−5)⋅(−3w​)=−10+5w3= -10 + \frac{5w}{3}=−10+35w​

STEP 4

Rewrite the original expression with the distributed terms:−10+5w3+73w−5-10 + \frac{5w}{3} + \frac{7}{3} w - 5−10+35w​+37​w−5 Combine like terms involving www:5w3+7w3=5w+7w3=12w3=4w\frac{5w}{3} + \frac{7w}{3} = \frac{5w + 7w}{3} = \frac{12w}{3} = 4w35w​+37w​=35w+7w​=312w​=4w

STEP 5

Combine the constant terms:−10−5=−15-10 - 5 = -15−10−5=−15

STEP 6

Combine the results from the previous steps:4w−154w - 154w−15Verify against the given options:4w−154w - 154w−15The simplified expression matches the option 4w−154w - 154w−15.4w−15\boxed{4w - 15}4w−15​

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Question2. Simplify the expression. $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$ $\frac{11}{3} w-15$ $\frac{11}{3} w-5$ $4 w-5$ $4 w-15$

1. The given expression is: $-5\left(2-\frac{w}{3}\right)+\frac{7}{3} w-5$
2. The goal is to simplify this expression to match one of the given options.
3. Simplification involves distributing, combining like terms, and reducing the expression properly.

1. Distribute the $-5$ through the term $\left(2-\frac{w}{3}\right)$ .
2. Combine like terms involving $w$ .
3. Combine the constant terms.
4. Verify the final simplified expression against the given options.

Distribute $-5$ through $\left(2-\frac{w}{3}\right)$ :
$-5 \left(2 - \frac{w}{3}\right) = -5 \cdot 2 + (-5) \cdot \left(-\frac{w}{3}\right)$
$= -10 + \frac{5w}{3}$

Rewrite the original expression with the distributed terms:
$-10 + \frac{5w}{3} + \frac{7}{3} w - 5$ Combine like terms involving $w$ :
$\frac{5w}{3} + \frac{7w}{3} = \frac{5w + 7w}{3} = \frac{12w}{3} = 4w$

Combine the constant terms:
$-10 - 5 = -15$

Combine the results from the previous steps:
$4w - 15$
Verify against the given options:
$4w - 15$
The simplified expression matches the option $4w - 15$ .
$\boxed{4w - 15}$