Answer to Question #343247 in Algebra for bkay

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.

$$3(2 – 3x) > 4(1 – 4x)$$

$$6-9x>4-16x$$

$$6-9x+16x-6>4-16x+16x-6$$

$$7x>-2$$

$$x>-\dfrac{2}{7}$$

$$x\in (-\dfrac{2}{7}, \infin)$$