Solved on Jan 10, 2024

Find the value of $w$ if $16=2(2w+w-1)$ .

STEP 1

Assumptions
1. The equation to solve is $16 = 2(2w + w - 1)$ .
2. We need to find the value of $w$ .

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.
$16 = 2(2w + w - 1)$

STEP 3

Apply the distributive property $a(b + c) = ab + ac$ to the terms inside the parentheses.
$16 = 2 \cdot 2w + 2 \cdot w - 2 \cdot 1$

STEP 4

Perform the multiplication for each term.
$16 = 4w + 2w - 2$

STEP 5

Combine like terms on the right side of the equation.
$16 = (4w + 2w) - 2$

STEP 6

Add the coefficients of $w$ .
$16 = 6w - 2$

STEP 7

To solve for $w$ , we need to isolate $w$ on one side of the equation. Start by adding 2 to both sides of the equation to move the constant term to the left side.
$16 + 2 = 6w - 2 + 2$

STEP 8

Perform the addition on both sides.
$18 = 6w$

STEP 9

Now, divide both sides of the equation by 6 to solve for $w$ .
$\frac{18}{6} = \frac{6w}{6}$

STEP 10

Calculate the division to find the value of $w$ .
$w = \frac{18}{6} = 3$
The solution to the equation $16 = 2(2w + w - 1)$ is $w = 3$ .

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Find the value of $w$ if $16=2(2w+w-1)$ .

STEP 1

Assumptions
1. The equation to solve is $16 = 2(2w + w - 1)$ .
2. We need to find the value of $w$ .

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.
$16 = 2(2w + w - 1)$

STEP 3

Apply the distributive property $a(b + c) = ab + ac$ to the terms inside the parentheses.
$16 = 2 \cdot 2w + 2 \cdot w - 2 \cdot 1$

STEP 4

Perform the multiplication for each term.
$16 = 4w + 2w - 2$

STEP 5

Combine like terms on the right side of the equation.
$16 = (4w + 2w) - 2$

STEP 6

Add the coefficients of $w$ .
$16 = 6w - 2$

STEP 7

To solve for $w$ , we need to isolate $w$ on one side of the equation. Start by adding 2 to both sides of the equation to move the constant term to the left side.
$16 + 2 = 6w - 2 + 2$

STEP 8

Perform the addition on both sides.
$18 = 6w$

STEP 9

Now, divide both sides of the equation by 6 to solve for $w$ .
$\frac{18}{6} = \frac{6w}{6}$

STEP 10

Calculate the division to find the value of $w$ .
$w = \frac{18}{6} = 3$
The solution to the equation $16 = 2(2w + w - 1)$ is $w = 3$ .

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Find the value of www if 16=2(2w+w−1)16=2(2w+w-1)16=2(2w+w−1).

STEP 1

Assumptions1. The equation to solve is 16=2(2w+w−1)16 = 2(2w + w - 1)16=2(2w+w−1).2. We need to find the value of www.

STEP 2

First, we need to distribute the 2 across the terms inside the parentheses.16=2(2w+w−1)16 = 2(2w + w - 1)16=2(2w+w−1)

STEP 3

Apply the distributive property a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac to the terms inside the parentheses.16=2⋅2w+2⋅w−2⋅116 = 2 \cdot 2w + 2 \cdot w - 2 \cdot 116=2⋅2w+2⋅w−2⋅1

STEP 4

Perform the multiplication for each term.16=4w+2w−216 = 4w + 2w - 216=4w+2w−2

STEP 5

Combine like terms on the right side of the equation.16=(4w+2w)−216 = (4w + 2w) - 216=(4w+2w)−2

STEP 6

Add the coefficients of www.16=6w−216 = 6w - 216=6w−2

STEP 7

To solve for www, we need to isolate www on one side of the equation. Start by adding 2 to both sides of the equation to move the constant term to the left side.16+2=6w−2+216 + 2 = 6w - 2 + 216+2=6w−2+2

STEP 8

Perform the addition on both sides.18=6w18 = 6w18=6w

STEP 9

Now, divide both sides of the equation by 6 to solve for www.186=6w6\frac{18}{6} = \frac{6w}{6}618​=66w​

STEP 10

Calculate the division to find the value of www.w=186=3w = \frac{18}{6} = 3w=618​=3The solution to the equation 16=2(2w+w−1)16 = 2(2w + w - 1)16=2(2w+w−1) is w=3w = 3w=3.

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Find the value of $w$ if $16=2(2w+w-1)$ .

Assumptions
1. The equation to solve is $16 = 2(2w + w - 1)$ .
2. We need to find the value of $w$ .

First, we need to distribute the 2 across the terms inside the parentheses.
$16 = 2(2w + w - 1)$

Apply the distributive property $a(b + c) = ab + ac$ to the terms inside the parentheses.
$16 = 2 \cdot 2w + 2 \cdot w - 2 \cdot 1$

Perform the multiplication for each term.
$16 = 4w + 2w - 2$

Combine like terms on the right side of the equation.
$16 = (4w + 2w) - 2$

Add the coefficients of $w$ .
$16 = 6w - 2$

To solve for $w$ , we need to isolate $w$ on one side of the equation. Start by adding 2 to both sides of the equation to move the constant term to the left side.
$16 + 2 = 6w - 2 + 2$

Perform the addition on both sides.
$18 = 6w$

Now, divide both sides of the equation by 6 to solve for $w$ .
$\frac{18}{6} = \frac{6w}{6}$

Calculate the division to find the value of $w$ .
$w = \frac{18}{6} = 3$
The solution to the equation $16 = 2(2w + w - 1)$ is $w = 3$ .