Alex is on a diet to lose some weight. he is losing weight at a rate of 2 pounds per week. after 6 weeks, he weighs 205 pounds. write and solve a linear equation to find how many weeks it will take alex to reach his target weight of 175 pounds.

Equation:  175 = -2x + 217

Solve for x:  x = 21 weeks

Step-by-step explanation:

Since Alex is losing weight at a consistent rate of 2 pounds per week, we can write a linear equation to represent his weight after a certain number of weeks.  Linear equations are typically written in the form: y = mx + b, where y = total, m = slope/rate, x = independent variable and b = initial value.  In this case, y = Alex's weight, m = rate of 2 pounds per week, x = number of weeks and b = Alex's initial weight.  Since we know that Alex loses 2 pounds per week and after 6 weeks he weighs 205, than we know that his original weight must be 205 + 12 (the number of pounds he's lost so far) = 217.  Now that we know all of our variable but 'x' (the number of weeks), we can set up our linear equation and solve:

175 = -2x + 217

Subtract 217 from both sides:  175 - 217 = -2x

Divide by -2 on both sides:  -42/-2 = -2x/-2

Solve for x:  x = 21 weeks