Solve for x 6 ( x − 2 ) = 8 ( x − 9 )

Mathematics

2 answers:

HACTEHA [7]3 years ago

8 0

X = 30 aaaaaaaaaaaaaaaaaaa

valentinak56 [21]3 years ago

4 0

Answer:

x = 30

Step-by-step explanation:

in order to solve for the value of x in the expression 6 ( x − 2 ) = 8 ( x − 9 )

we will first of all open the brackets and then evaluate for the value of x by combining the like terms.

from 6 ( x − 2 ) = 8 ( x − 9 )

6x -12 = 8x -72

combine the like terms

6x - 12 + 72 = 8x

-12 + 72 = 8x -6x

60 = 2x

divide both sides by the coefficient of x which is 2

60/2 = 2x/2

30 = x

x = 30

therefore the value of x in the expression 6 ( x − 2 ) = 8 ( x − 9 ) is equals to 30

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Determine the arithmetic sequence if the fourth term is negative six and the eleventh term is negative thirty four

ICE Princess25 [194]

An arithmetic sequence takes the form

$a_n=a_{n-1}+d$

where $d$ is the common difference between terms. You can solve for $a_n$ in terms of any of the previous terms of the sequence:

$a_n=a_{n-1}+d\implies~a_n=a_{n-2}+2d\implies~a_n=a_{n-3}+3d\implies\cdots\implies~a_n=a_{n-k}+kd$

for some integer $1\le k\le n-1$

Continuing in this way, you know that the sequence can be defined explicitly in terms of the first term $a_1$

$a_n=a_1+(n-1)d$

Given that the 4th term is $a_4=-6$ and the 11th term is $a_{11}=-34$ , you have the following system of equations.

$\begin{cases}-6=a_1+(4-1)d\\-34=a_1+(11-1)d\end{cases}$

Solving this system for the two unknowns yields $a_1=6$ and $d=-4$ .

So, the sequence is given explicitly by

$a_n=6+(n-1)(-4)=-4n+5$