Mathematics, 20.09.2019 23:00 ddwithdadarco

How many solutions exist for given equation?
1/2)x+12=4x-1

Answers: 1

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Answer from: isabellatessa86

There is one solution for the equation.

Exact Form:

$x=\frac{26}{7}$

Decimal Form:

x=3.714285...

Mixed Number Form:

$x=3\frac{5}{7}$

Step-by-step explanation:

Combine $\frac{1}{2}$ and x.

$\frac{x}{2} +12=4x-1$

Move all terms containing x to the left side of the equation.

Subtract 4x from both sides of the equation.

$\frac{x}{2} +12-4x=-1$

Simplify the left side of the equation.

To write $\frac{-4x}{1}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} +\frac{-4x}{1} *\frac{2}{2} +12=-1$

Write each expression with a common denominator of 2, by multiplying each by an appropriate factor of 1.

Combine

$\frac{x}{2}+\frac{-4x*2}{1*2} +12=-1$

Multiply 2 by 1.

$\frac{x}{2} +\frac{-4x*2}{2} +12=-1$

Combine the numerators over the denominator.

$\frac{x-4x*2}{2} +12=-1$

Simplify each term

Simplify the numerator

Factor x out of x - 4x * 2

Raise x to the power of 1.

$\frac{x-4x*2}{2} +12=-1$

Factor x out of $x^{1}$

$\frac{x*1-4x*2}{2} +12=-1$

Factor x out of -4x * 2

$\frac{x*1+x(-4*2)}{2} +12=-1$

Factor x out of x * 1 + x (-4 * 2).

$\frac{x(1-4*2)}{2} +12=-1$

Multiply -4 by 2.

$\frac{x(1-8)}{2} +12=-1$

Subtract 8 from 1.

$\frac{x*-7}{2} +12=-1$

Move -7 to the left of x.

$\frac{-7*x}{2} +12=-1$

Move the negative in front of the fraction.

$-\frac{7x}{2} +12=-1$

Move all terms not containing x to the right side of the equation.

Subtract 12 from both sides of the equation.

$-\frac{7x}{2} =-1-12$

Subtract 12 from -1.

$-\frac{7x}{2} =-13$

Multiply both sides of the equation by $-\frac{2}{7}$ .

$-\frac{2}{7} *(-\frac{7x}{2})=-\frac{2}{7} *-13$

Simplify both sides of the equation.

Simplify the left side

Cancel the common factor of 2.

Move the leading negative in $-\frac{2}{7}$ into the numerator.

$\frac{-2}{7} *-\frac{7x}{2} =-\frac{2}{7} *-13$

Move the leading negative in $-\frac{7x}{2}$ into the numerator.

$\frac{-2}{7} *\frac{-7x}{2} =-\frac{2}{7} *-13$

Factor out the greatest common factor 2.

$\frac{2*-1}{7} *\frac{-7x}{2*1} =-\frac{2}{7} *-13$

Cancel the common factor

$\frac{-1}{7} \frac{-7x}{1} =-\frac{2}{7} *-13$

Cancel the common factor of 7.

Factor out the greatest common factor 7.

$\frac{-1}{7(1)} *\frac{7(-x)}{1} =-\frac{2}{7} *-13$

Cancel the common factor.

$\frac{-1}{1} *\frac{-x}{1} =-\frac{2}{7} *-13$

Simplify

Multiply $\frac{-1}{1}$ and $\frac{-x}{1}$ .

$\frac{x}{1} =-\frac{2}{7} *-13$

Multiply -1 by -1.

$\frac{1x}{1} =-\frac{2}{7} *-13$

Multiply x by 1.

$\frac{x}{1} =-\frac{2}{7} *-13$

Divide x by 1.

$x=-\frac{2}{7} *-13$

Multiply $-\frac{2}{7} * -13$

Multiply -13 by -1.

$x=13(\frac{2}{7} )$

Combine 13 and $\frac{2}{7}$ .

$x=\frac{13*2}{7}$

Multiply 13 by 2.

$x = \frac{26}{7}$

The result can be shown in multiple forms.

Exact Form:

$x=\frac{26}{7}$

Decimal Form:

x=3.714285...

Mixed Number Form:

$x=3\frac{5}{7}$

Answer from: Quest

62926281916 inches of rain: )

Answer from: Quest

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

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How many solutions exist for given equation?
1/2)x+12=4x-1...