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4 years ago

An equation is shown below. 12 – 6(w – 3) = 3(– 5 – 3w) + 21 Enter the solution of w for this equation.

1 answer:

5 0

<span>Simplifying
12 + -6(w + -3) = 3(-5 + -3w) + 21

Reorder the terms:
12 + -6(-3 + w) = 3(-5 + -3w) + 21
12 + (-3 * -6 + w * -6) = 3(-5 + -3w) + 21
12 + (18 + -6w) = 3(-5 + -3w) + 21

Combine like terms: 12 + 18 = 30
30 + -6w = 3(-5 + -3w) + 21
30 + -6w = (-5 * 3 + -3w * 3) + 21
30 + -6w = (-15 + -9w) + 21

Reorder the terms:
30 + -6w = -15 + 21 + -9w

Combine like terms: -15 + 21 = 6
30 + -6w = 6 + -9w

Solving
30 + -6w = 6 + -9w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '9w' to each side of the equation.
30 + -6w + 9w = 6 + -9w + 9w

Combine like terms: -6w + 9w = 3w
30 + 3w = 6 + -9w + 9w

Combine like terms: -9w + 9w = 0
30 + 3w = 6 + 0
30 + 3w = 6

Add '-30' to each side of the equation.
30 + -30 + 3w = 6 + -30

Combine like terms: 30 + -30 = 0
0 + 3w = 6 + -30
3w = 6 + -30

Combine like terms: 6 + -30 = -24
3w = -24

Divide each side by '3'.
w = -8

Simplifying
w = -8</span>

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Hope this helps :D

7 0

4 years ago

Read 2 more answers

Which expressions are equivalent to 2 (three-fourths x 7) minus 3 (one-half x minus 5)? Check all that apply. -1 29 2 (three-fou

Otrada [13]

The expression is equivalent to $\rm2( \dfrac{3}{4}x) + 2(7) -3(\dfrac{1}{2}x) + (-3) (-5)\\$ .

<h2 /><h2>Given that</h2>

Expression; $\rm 2(\dfrac{3}{4}x+7) -3(\dfrac{1}{2}x-5)$

<h3>We have to determine</h3>

Which expressions are equivalent to the given expression.

<h3>According to the question</h3>

Expression; $\rm 2(\dfrac{3}{4}x+7) -3(\dfrac{1}{2}x-5)$

To solve the given expression follow all the steps given below.

By applying the distributive property of multiplication;

$\rm a(b+c) = ab+ac$

Then,

The equivalent expression is,

$\rm 2(\dfrac{3}{4}x+7) -3(\dfrac{1}{2}x-5)\\
\\
\rm (2 \times \dfrac{3}{4}x) + 2(7) -3(\dfrac{1}{2}x) + (-3) (-5)\\
\\
2( \dfrac{3}{4}x) + 2(7) -3(\dfrac{1}{2}x) + (-3) (-5)\\$

Hence, the expression is equivalent to $\rm2( \dfrac{3}{4}x) + 2(7) -3(\dfrac{1}{2}x) + (-3) (-5)\\$ .

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2 years ago

What is the equation for the axis of symmetry of your quadratic ? <br> Y=x^2-4x

vekshin1

Answer:

$y = {x}^{2} - 4x \\ y = x(x - 4)$

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3 years ago

Kym plans to deposit $100 in an account at the end of each month for the next five years so that she can take a trip. (a) If Kym

yaroslaw [1]

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Monthly deposit= $100

Interest rate= 0.06/12= 0.005

Number of periods= 12*5= 60 months

<u>To calculate the future value, we need to use the following formula:</u>

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {100*[(1.005^60) - 1]} / 0.005

FV= $6,977

b) <u>If the deposit is at the beginning of the month, the interest is compounded one more period</u>. We need to use the following formula:

FV= {A*[(1+i)^n-1]}/i + {[A*(1+i)^n]-A}

FV= 6,977 + {[100*(1.005^60)] - 100}

FV= 6,977 + 35

FV= $7,012

3 0

3 years ago

Simplify. 12k - 6 + (3k)(4) Is it -6, 6, 24k + 6, or 24k - 6?

Effectus [21]

It's 24k-6

By order of operations, you do the multiplication first: 3k(4) = 12k

12k-6+12k now combine like terms

24k-6

Hope that helps

7 0

3 years ago