Question

A.] Given the equation 7(x + 2) = 2x − 1, solve for the variable. Explain each step and justify your process.

B.] Jeff solved a similar equation below. Is Jeff's solution correct? Explain why or why not.
3x − 2 = 5(x + 2)
3x − 2 = 5x + 10
8x = 8
x = 1

Answer 1

`A.\\7(x+2)=2x-1\ \ \ |use\ distributive\ property\ a(b+c)=ab+ac\\\\7(x)+7(2)=2x-1\\\\7x+14=2x-1\ \ \ \ |subtract\ 2x\ from\ both\ sides\\\\5x+14=-1\ \ \ \ \ |subtract\ 14\ from\ both\ sides\\\\5x=-15\ \ \ \ \ |divide\ both\ sides\ by\ 5\\\\\boxed{x=-3}`



`B.\ Jeff's\ solution\ is\ incorrect\\\\3x-2=5(x+2)\\\\3x-2=5x+10\ \ \ \ \ |OK\\\\\underline{8x=8}\ \ \ \ |WRONG\\\\correct\\\\3x-2=5x+10\ \ \ \ |subtract\ 5x\ from\ both\ sides\ and\ add\ 2\ to\ both\ sides\\\\-2x=12\ \ \ \ \ \ |divide\ both\ sides\ by\ (-2)\\\\\boxed{x=-6}`


`check:\\subtitute\ x=1\\\\L=3(1)-2=3-2=1\\R=5(1+2)=5(3)=15\\L\\eq R!!!\\\\subtitute\ x=-6\\\\L=3(-6)-2=-18-2=-20\\R=5(-6+2)=5(-4)=-20\\L=R\ :)`