Respuesta :
Answer:
One solution.
Step-by-step explanation:
1/2x + 12 = 4x - 1
12 + 1 = 4x - 1/2 x
13 = 7/2 x
x = 13 *2/7 = 26/7.
Answer:
There is one solution for the equation.
Exact Form:
[tex]x=\frac{26}{7}[/tex]
Decimal Form:
[tex]x=3.714285...[/tex]
Mixed Number Form:
[tex]x=3\frac{5}{7}[/tex]
Step-by-step explanation:
Combine [tex]\frac{1}{2}[/tex] and x.
[tex]\frac{x}{2} +12=4x-1[/tex]
Move all terms containing x to the left side of the equation.
Subtract 4x from both sides of the equation.
[tex]\frac{x}{2} +12-4x=-1[/tex]
Simplify the left side of the equation.
To write [tex]\frac{-4x}{1}[/tex] as a fraction with a common denominator, multiply by [tex]\frac{2}{2}[/tex].
[tex]\frac{x}{2} +\frac{-4x}{1} *\frac{2}{2} +12=-1[/tex]
Write each expression with a common denominator of 2, by multiplying each by an appropriate factor of 1.
Combine
[tex]\frac{x}{2}+\frac{-4x*2}{1*2} +12=-1[/tex]
Multiply 2 by 1.
[tex]\frac{x}{2} +\frac{-4x*2}{2} +12=-1[/tex]
Combine the numerators over the denominator.
[tex]\frac{x-4x*2}{2} +12=-1[/tex]
Simplify each term
Simplify the numerator
Factor x out of x - 4x * 2
Raise x to the power of 1.
[tex]\frac{x-4x*2}{2} +12=-1[/tex]
Factor x out of [tex]x^{1}[/tex]
[tex]\frac{x*1-4x*2}{2} +12=-1[/tex]
Factor x out of -4x * 2
[tex]\frac{x*1+x(-4*2)}{2} +12=-1[/tex]
Factor x out of x * 1 + x (-4 * 2).
[tex]\frac{x(1-4*2)}{2} +12=-1[/tex]
Multiply -4 by 2.
[tex]\frac{x(1-8)}{2} +12=-1[/tex]
Subtract 8 from 1.
[tex]\frac{x*-7}{2} +12=-1[/tex]
Move -7 to the left of x.
[tex]\frac{-7*x}{2} +12=-1[/tex]
Move the negative in front of the fraction.
[tex]-\frac{7x}{2} +12=-1[/tex]
Move all terms not containing x to the right side of the equation.
Subtract 12 from both sides of the equation.
[tex]-\frac{7x}{2} =-1-12[/tex]
Subtract 12 from -1.
[tex]-\frac{7x}{2} =-13[/tex]
Multiply both sides of the equation by [tex]-\frac{2}{7}[/tex].
[tex]-\frac{2}{7} *(-\frac{7x}{2})=-\frac{2}{7} *-13[/tex]
Simplify both sides of the equation.
Simplify the left side
Cancel the common factor of 2.
Move the leading negative in [tex]-\frac{2}{7}[/tex] into the numerator.
[tex]\frac{-2}{7} *-\frac{7x}{2} =-\frac{2}{7} *-13[/tex]
Move the leading negative in [tex]-\frac{7x}{2}[/tex] into the numerator.
[tex]\frac{-2}{7} *\frac{-7x}{2} =-\frac{2}{7} *-13[/tex]
Factor out the greatest common factor 2.
[tex]\frac{2*-1}{7} *\frac{-7x}{2*1} =-\frac{2}{7} *-13[/tex]
Cancel the common factor
[tex]\frac{-1}{7} \frac{-7x}{1} =-\frac{2}{7} *-13[/tex]
Cancel the common factor of 7.
Factor out the greatest common factor 7.
[tex]\frac{-1}{7(1)} *\frac{7(-x)}{1} =-\frac{2}{7} *-13[/tex]
Cancel the common factor.
[tex]\frac{-1}{1} *\frac{-x}{1} =-\frac{2}{7} *-13[/tex]
Simplify
Multiply [tex]\frac{-1}{1}[/tex] and [tex]\frac{-x}{1}[/tex].
[tex]\frac{x}{1} =-\frac{2}{7} *-13[/tex]
Multiply -1 by -1.
[tex]\frac{1x}{1} =-\frac{2}{7} *-13[/tex]
Multiply x by 1.
[tex]\frac{x}{1} =-\frac{2}{7} *-13[/tex]
Divide x by 1.
[tex]x=-\frac{2}{7} *-13[/tex]
Multiply [tex]-\frac{2}{7} * -13[/tex]
Multiply -13 by -1.
[tex]x=13(\frac{2}{7} )[/tex]
Combine 13 and [tex]\frac{2}{7}[/tex].
[tex]x=\frac{13*2}{7}[/tex]
Multiply 13 by 2.
[tex]x = \frac{26}{7}[/tex]
The result can be shown in multiple forms.
Exact Form:
[tex]x=\frac{26}{7}[/tex]
Decimal Form:
[tex]x=3.714285...[/tex]
Mixed Number Form:
[tex]x=3\frac{5}{7}[/tex]
