Answer to Question #343473 in Discrete Mathematics for Bethsheba Kiap

Question

Solve the inequalities. Give your answer in interval notation, and indicate the answer

geometrically on the real-number line.

a. t + 6 ≤ 2 + 3t

b. 3(2 – 3x) > 4(1 – 4x)

Answer 1

a.

$$t + 6\le 2 + 3t$$ $$3t-t\ge6-2$$ $$2t\ge4$$ $$t\ge 2$$

$t\in [2, \infin)$

b.

$$3(2 – 3x) > 4(1 – 4x)$$ $$6-9x>4-16x$$ $$6-9x+16x-6>4-16x+16x-6$$ $$7x>-2$$ $$x>-\dfrac{2}{7}$$ $$x\in (-\dfrac{2}{7}, \infin)$$