Question

Solve for k 5/8(3k+1)-1/4(7k+2)=1

Answer 1

k = 7

Explanation:

`(5)/(8)(3k+1)-(1)/(4)(7k+2)=1\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup^1\cdot(5)/(8\!\!\!\!\diagup_1)(3k+1)-8\!\!\!\!\diagup^2\cdot(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`