Answer:
k = 11.87
Step-by-step explanation:
Because the two expressions should be equivalent, set the two expressions equal to each other.
[tex]-10.5x+k=-2.1(5x-3.7)+4.1[/tex]
Begin simplifying the equation and solve for k.
[tex]-10.5x+k=-10.5x+7.77+4.1[/tex] (distributive property)
[tex]-10.5x+k=-10.5x+11.87[/tex] (combine like terms - 7.77 + 4.1)
[tex]k = 11.87[/tex] (add 10.5x to both sides to combine like terms -- the x values cancel out because -10.5x+10.5x = 0. Therefore, you are left with k = 11.87)
