Answer:
k = 7
Step-by-step explanation:
[tex]\dfrac{5}{8}(3k+1)-\dfrac{1}{4}(7k+2)=1\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup^1\cdot\dfrac{5}{8\!\!\!\!\diagup_1}(3k+1)-8\!\!\!\!\diagup^2\cdot\dfrac{1}{4\!\!\!\!\diagup_1}(7k+2)=8\cdot1\\\\5(3k+1)-2(7k+2)=8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(5)(3k)+(5)(1)+(-2)(7k)+(-2)(2)=8\\\\15k+5-14k-4=8\qquad\text{combine like terms}\\\\(15k-14k)+(5-4)=8\\\\k+1=8\qquad\text{subtract 1 from both sides}\\\\k=7[/tex]
