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zloy xaker [14]
1 year ago
8

Solve for x: 3x+2(x-1)=9x+4

Mathematics
2 answers:
VARVARA [1.3K]1 year ago
8 0

Answer:

x = -3/2

Step-by-step explanation:

1) Expand.

3x+2x-2=9x+4

2) Simplify 3x+2x-2 to 5x-2.

5x-2=9x+4

3) Subtract 5x from both sides.

-2=9x+4-5x

4) Simplify 9x+4-5x to 4x+4.

-2=4x+4

5) Subtract 4 from both sides.

-2-4=4x

6) Simplify - 2 - 4 to -6.

-6=4x

7) Divide both sides by 4.

-6/4 = x

8) Simplify 6/4 to 3/2.

-3/2 = x

9) Switch sides.

x = -3/2

bixtya [17]1 year ago
3 0

Answer:

x = -1.5

Step-by-step explanation:

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The sequence forms a Geometric sequence as the rule to obtain the value for the next term is by ratio

Term 1: 1000
Term 2: 200
Term 3: 40

From term 1 to term 2, there's a decrease by \frac{1}{5}
From term 2 to term 3, there's a decrease also by \frac{1}{5}

The rule to find the n^{th} term in a sequence is 
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So, the formula for the sequence in question is
n_{th} term = 1000( \frac{1}{5} ^{n-1} )

The sequence is a divergent one. We can always find the value of the next term by dividing the previous term by 5 and if we do that, the value of the next term will get closer to 'zero' but never actually equal to zero.

We can find a partial sum of the sequence using the formula
S_{∞} = \frac{a}{1-r} for -1<r<1 
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And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:

6.5\mleft(8x+6\mright)

You can identify that the word "combined" indicates that that expression was obtained by adding both areas.

Knowing the above, you can set up the following equation:

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Where "A" is the area of the walkway around the rectangular garden.

Solving for "A", you get the following expression:

\begin{gathered} A=6.5(8x+6)-6(6.5x+2.5) \\ A=52x+39-39x-15 \\ A=13x+24 \end{gathered}

The answer is:

13x+24

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