Question

Solve the inequality by graphing each of the lines. Check your answer by solving algebraically. 4x + 1 < 1/2x +3

A) y = 8x - 2
B) y = 6x - 4
C) y = -6x + 4
D) y = -8x + 2

Answer 1

The correct answer is option A) y = 8x - 2. To solve the inequality 4x + 1 < 1/2x + 3, we can graph the lines represented by the options and find the intersection point. Alternatively, we can solve the inequality algebraically and find x < 4/7 as the solution.

Step-by-step explanation:

The correct answer is option A) y = 8x - 2.

To solve the inequality 4x + 1 < 1/2x + 3 by graphing, we need to find the intersection point of the two lines. The line represented by option A, y = 8x - 2, has a slope of 8 and a y-intercept of -2. The line represented by option B, y = 6x - 4, has a slope of 6 and a y-intercept of -4. We can graph these lines and find the point where they intersect.

Algebraically, we can solve the inequality:

4x + 1 < 1/2x + 3

First, we can multiply both sides of the inequality by 2 to get rid of the fraction:

8x + 2 < x + 6

Next, we can subtract x from both sides of the inequality:

7x + 2 < 6

Then, we can subtract 2 from both sides of the inequality:

7x < 4

Finally, we can divide both sides of the inequality by 7:

x < 4/7

So the solution to the inequality is x < 4/7.