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Alex777 [14]
1 year ago
13

Solve the following equation: 2|3x - 2| -4 = 16

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

Answer:

x=6 and -14/3

Step-by-step explanation:

Divide 2:

|3x - 2|-4 = 16

Plus 4: |3x - 2| = 16

So 3x - 2=16 and -3x + 2=16

3x - 2=16: x=6

-3x + 2=16: x=-14/3

umka21 [38]1 year ago
7 0

Hi there,

I hope you and your family are staying safe and healthy!

Let's solve the equation

2|3x -2| -4 = 16

The first step here is to add 4 on both sides

2(|3x-2|)-4+4=16+4\\=2(|3x-2|)=20

We're not done yet! So now we need to divide both sides by 2

\frac{2(|3x-2|)}{2} = \frac{20}{2}

=|3x-2|=10

Now we need to solve for the absolute value

We know either 3x - 2 = 10 or 3x-2=-10

Therefore, there are two possibilities here.

<h2>Possibility 1</h2>

3x - 2 = 10 \\3x = 10 + 2\\3x = 12\\x = 12/3\\x = 4

<h2>Possibility 2</h2>

3x - 2 = -10\\3x = -10 + 2 \\3x = -8\\x = -8/3\\

Thus,

The answer is: x = 4 or x = \frac{-8}{3}

Happy to help! I wish you all the best this semester :)

-Garebear

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7 0
3 years ago
Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9
nalin [4]

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B  

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = \left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]  = 1(1-4) - 2(2-6) + 3(4 - 3)

                    = 1(-3) - 2(-4) + 3(1)

                    = -3+8+3 = 8

also D\neq 0

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx =  \left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]   = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = \frac{Dx}{D}  = \frac{16}{8} = 2

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y = \frac{Dy}{D} = 0

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so we have the solution as

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Answer:

I hope it's helpful for you

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