Answer :
The number that satisfies the given equation is [tex]x = 6[/tex].
To solve the given problem, we need to find the number that satisfies the equation described in the problem statement:
"Eleven more than four times a number is equal to the difference between 59 and four times the number."
Let's define the unknown number as [tex]x[/tex].
Step-by-Step Solution:
According to the problem, eleven more than four times the number is represented by:
[tex]4x + 11[/tex]The difference between 59 and four times the number is represented by:
[tex]59 - 4x[/tex]We set up the equation by stating that these two expressions are equal:
[tex]4x + 11 = 59 - 4x[/tex]To isolate the variable [tex]x[/tex], we first add [tex]4x[/tex] to both sides to get rid of the [tex]-4x[/tex] term on the right side:
[tex]4x + 4x + 11 = 59 - 4x + 4x[/tex]
This simplifies to:
[tex]8x + 11 = 59[/tex]Next, we subtract 11 from both sides to isolate the [tex]8x[/tex] term:
[tex]8x + 11 - 11 = 59 - 11[/tex]
This simplifies to:
[tex]8x = 48[/tex]Finally, we divide both sides by 8 to solve for [tex]x[/tex]:
[tex]\frac{8x}{8} = \frac{48}{8}[/tex]
This simplifies to:
[tex]x = 6[/tex]
