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2 years ago

Solve for x: two thirds(x − 2) = 4x.

Mathematics

1 answer:

Sveta_85 [38]2 years ago

5 0

Answer:

$x = - 0.4$

Step-by-step explanation:

$\frac{2}{3} (x - 2) = 4x$

Expand with the distributive rule:

$\frac{2}{3} x - \frac{2}{3} \times 2 = 4x$

$\frac{2}{3} x - \frac{4}{3} = 4x$

Add 4/3 to both sides:

$\frac{2}{3} x = 4x + \frac{4}{3}$

Subtract 4x from both sides

$- \frac{10}{3} x = \frac{4}{3}$

$- 10x = 4$

$x = - 0.4$

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Kimberly makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of her co

Gala2k [10]

Answer:

third choice : Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.

You’re welcome ;)

7 0

2 years ago

Consider the function f(x)=3x-1 (over)x+4 (a) At which value of x will the function not have a solution? Explain your answer. (b

Irina18 [472]

Ans(a):

Given function is $f(x)=\frac{3x-1}{x+4}$

we know that any rational function is not defined when denominator is 0 so that means denominator x+4 can't be 0

so let's solve

x+4≠0 for x

x≠0-4

x≠-4

Hence at x=4, function can't have solution.

Ans(b):

We know that vertical shift occurs when we add something on the right side of function so vertical shift by 4 units means add 4 to f(x)

so we get:

g(x)=f(x)+4

$g(x)=\frac{3x-1}{x+4}+4$

We may simplify this equation but that is not compulsory.

Comparision:

Graph of g(x) will be just 4 unit upward than graph of f(x).

Ans(e):

To find value of x when g(x)=8, just plug g(x)=8 in previous equation

$8=\frac{3x-1}{x+4}+4$

$8-4=\frac{3x-1}{x+4}$

$4=\frac{3x-1}{x+4}$

$4(x+4)=(3x-1)$

$4x+16=3x-1$

4x-3x=-1-16

x=-17

Hence final answer is x=-17

8 0

3 years ago

What are the zeros of (x-2)(x^2-9)

WARRIOR [948]

$(x-2)(x^2-9)=0\iff x-2=0\ or\ x^2-9=0\\\\x-2=0\ \ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=2}\\\\x^2-9=0\ \ \ \ |add\ 9\ to\ both\ sides\\\\x^2=9\iff x=\pm\sqrt9\to \boxed{x=-3\ or\ x=3}\\\\Answer:\boxed{x=-3\ or\ x=2\ or\ x=3}$