Question

6) Solve the inequality. Write the answer using both set-builder notation and interval notation. Graph the solution set on a number line. Multiply both sides of the inequality by the LCD first to clear fractions. -3/4 x≤9

Answer 1

given: -3/4 x≤9

by multiplying with 4 both side of inequality

(-3 * 4/4)*x ≤(9*4)

(-3)x≤(36)

now divide both side by 3

(-3/3)x≤(36/3)

(-1)x≤(12)

now multiply with -1 both side and change the sign of inequality also, because when we multiply with negative number in equality changes.

x (-12)

so this is final solution:

set- builder notation:   "the solution set is { x | x is a real number and (greater than or equal to -12) or  x (-12) }".

interval notation: x [ -12, + )