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.

$3(2 – 3x) > 4(1 – 4x)$

$6-9x>4-16x$

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

$7x>-2$

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

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