contestada

Solve the inequality a, b, c for brainliest and 30 points
a) 3x - 8 > 16

b) 2x-1 < 9

c)) Write down all the integers that satisfy both inequalities shown in part (a)
and (b).

Respuesta :

mathstudent55

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.

mirai123

Answer:

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

b)[tex]\{x\in \mathbb{R}|x<5 \}[/tex] or just [tex]x<5[/tex], or [tex](-\infty, 5)[/tex]

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

Step-by-step explanation:

a) [tex]3x - 8 > 16[/tex]

[tex]3x - 8 +8> 16+8\\3x>24\\[/tex]

[tex]$\frac{3x}{3}>\frac{24}{3} $[/tex]

[tex]x>8[/tex]

Interval notation: [tex]\left(8,\:\infty \:\right)[/tex]

[tex]\{x\in \mathbb{R}|x>8 \}[/tex]

b) [tex]2x-1 < 9[/tex]

[tex]2x-1 +1< 9+1\\2x<10\\x<5[/tex]

Interval notation: [tex](-\infty, 5)[/tex]

[tex]\{x\in \mathbb{R}|x<5 \}[/tex]

c) The integers that satisfy both inequalities:

[tex](-\infty, 5)\cap \left(8,\:\infty \:\right) = \emptyset[/tex]

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

Otras preguntas