Set x to 1.5 and substitute it into the inequality to obtain y = 4. Therefore, the point (1.5, 4) lies on the specified line.
One particular solution for the inequality 8x-3y<12 can be found by first rewriting the inequality in slope-intercept form. This form is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept. To find m and b, we can perform the following steps:
Move the x term to the other side of the inequality:
-3y < -8x + 12
Divide both sides of the inequality by -3:
y > (8/3)x - 4
Rewrite the inequality in slope-intercept form:
y = (8/3)x - 4
Now that we have the equation in slope-intercept form, we can choose any value for x and solve for y to find one particular solution. For example, let's choose x = 1.5. Substituting this value into the equation, we get:
y = (8/3)(1.5) - 4
y = 4
Therefore, one particular solution for the inequality 8x-3y<12 is x = 1.5 and y = 4.
In addition to this particular solution, there are infinitely many other solutions to the inequality. This is because the inequality represents an entire shaded region on the coordinate plane. Any point within this region is a valid solution.
Complete question below:
Find one particular solution for the inequality 8x-3y<12.