Solve for x: 3x – 2(6 - x) = 7x + 2(5 + x) – 6

Mathematics

1 answer:

MAVERICK [17]2 years ago

4 0

Answer:

-4

Step-by-step explanation:

3x-2(6-x)=7x+2(5+x)-6

First, distribute.

3x+ −12+ 2x = 7x + 10 + 2x −6

Combine like terms on each side.

5x − 12= 9x + 4

To solve for x, pick a side to solve. I will solve the right x.

5x - 12 = 9x + 4

-5x -5x

-12 = 4x + 4

Subtract 4 to isolate the variable.

-16 = 4x

Divide 4.

-4 = x

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2. Assume f(x) = g(x). Which of the following functions may be used to represent the equation 3x+2 = 7x + 6? A. f(x) = x + 2, g(

charle [14.2K]

Answer:

C. f(x) = 3·x + 2, g(x) = 7·x + 6

Step-by-step explanation:

The given equations relates to the property of equality of values;

The given formula for the association between f(x) and g(x) is f(x) = g(x)

The given equation of two expressions is 3·x + 2 = 7·x + 6

By transitive property of equality, the two above equations are correct when f(x) = 3·x + 2 and g(x) = 7·x + 6

Therefore, the function that may be used to represent the equation is option C; f(x) = 3·x + 2, g(x) = 7·x + 6.

7 0

3 years ago

What is 04.151515... into a fraction

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)