Question

Solve the inequality a, b, c for brainliest and 30 points

Answer 1

Answer:

See below.

Step-by-step explanation:

a)

3x - 8 > 16

3x > 24

x > 8

b)

2x - 1 < 9

2x < 10

x < 5

c)

There are no integers that satisfy both inequalities since there is no number that is both greater than 8 and less than 5.

Answer 2

Answer:

a) $\{x\in \mathbb{R}|x>8 \}$ or just $x>8$, or $\left(8,\:\infty \:\right)$

b)$\{x\in \mathbb{R}|x$ or just $x$, or $(-\infty, 5)$

c) There's no integer that satisfy both inequalities.

Step-by-step explanation:

a) $3x - 8 > 16$

$3x - 8 +8> 16+8\\3x>24$

$\frac{3x}{3}>\frac{24}{3}$

$x>8$

Interval notation: $\left(8,\:\infty \:\right)$

$\{x\in \mathbb{R}|x>8 \}$

b) $2x-1 < 9$

$2x-1 +1< 9+1\\2x$

Interval notation: $(-\infty, 5)$

$\{x\in \mathbb{R}|x$

c) The integers that satisfy both inequalities:

$(-\infty, 5)\cap \left(8,\:\infty \:\right) = \emptyset$

<---------------- 5 ---------------- 8 ------------------->