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4 years ago

-2(3x+9)=-54 AND 2(3x+4) -3x=35 SHOW WORK PLEASE

Mathematics

1 answer:

Naily [24]4 years ago

5 0

Answer:

1. x=6

2. x=9

Step-by-step explanation:

$-2(3x+9)=-54\\-6x-18=-54\\+18 +18\\-6x=-36\\\frac{-6x}{-6} = \frac{-36}{-6}\\x=6$

$2(3x+4)-3x=35\\6x+8-3x=35\\3x+8=35\\-8 -8\\3x=27\\\frac{3x}{3} =\frac{27}{3} \\x=9$

<u>Written Explanation: </u>

-2x(3x+9)=-54

-6x-`8=54 (Distributive property)

Add 18 to both sides

-6x=-36

Divide both sides by -6 (negative divided by a negative equals a positive)

x=6

2(3x+4)-3x=35

6x+8-3x=35 (distributive property)

3x+8=35 (combine Iike terms and then subtract them 6x-3x=3x)

Subtract 8 from both sides

3x=27

Divide both sides by 3

x=9

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The minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

<h3>The minimum and maximum percentages of voters in Republicans? Green?</h3>

The attached circle graph represents the missing information in the question.

From the graph, we have:

Republicans = 42%

Green = 2%

The actual percentage is given as: ±2%

So, we have:

Republicans = 42% ± 2% = (40%, 44%)

Green = 2% ± 2% = (0%, 4%)

Hence, the minimum and maximum percentages of voters who could vote Republicans are 40% and 44% respectively, while Green are 0% and 4%

<h3>The absolute value equations of part (a)?</h3>

We have:

The actual percentage is given as: ±2%

Let the number of votes be on the circle graph be x and the range be y.

So, we have:

y - x = ±2%

Express as absolute value equation

|y - x| = 2%

For Republicans, we have:

|y - 42%| = 2%

For Green, we have:

|y - 2%| = 2%

Hence, the absolute value equations are |y - 42%| = 2% and |y - 2%| = 2%

<h3>The party of candidate that receives 44% vote</h3>

In (a), we have:

Republicans = 42% ± 2% = (40%, 44%)

Hence, the party of candidate that receives 44% vote is Republican