Answer:
Inequality notation: [tex]x<4\:[/tex]
Interval Notation: [tex]\left(-\infty \:,\:4\right)[/tex]
The graph of the solution set on the number line is also attached below.
Step-by-step explanation:
Given the inequality
[tex]10x<2+2\left(-3x+31\right)[/tex]
[tex]10x<-6x+64[/tex] ∵ [tex]\mathrm{Expand\:}2+2\left(-3x+31\right):\quad -6x+64[/tex]
[tex]\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}[/tex]
[tex]10x+6x<-6x+64+6x[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]16x<64[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}16[/tex]
[tex]\frac{16x}{16}<\frac{64}{16}[/tex]
[tex]x<4[/tex]
so
- Inequality notation: [tex]x<4\:[/tex]
- Interval Notation: [tex]\left(-\infty \:,\:4\right)[/tex]
Therefore,
[tex]10x<2+2\left(-3x+31\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:4\right)\end{bmatrix}[/tex]
The graph of the solution set on the number line is also attached below.
