Question

Inequalities

Solve the inequality 10% < 2 + 2( - 3.+ 31). Write your answer as an inequality and in interval
notation, then graph the solution set on the number line.
For Graphing: If the symbol in the inequality is < or > , use an open circle. If the symbol in the
inequality is < or >, use a closed circle.
Inequality: 10x < 2 + 2( - 3x + 31)
Inequality Notation
Graph
Interval Notation
10
5
Preview
-5 0
Clear All Draw: 7
Preview
.
Get help: Video

Answer 1

Inequality notation:
`x<4\:`

Interval Notation:
`\left(-\infty \:,\:4\right)`

The graph of the solution set on the number line is also attached below.

Explanation:

Given the inequality

`10x<2+2\left(-3x+31\right)`

`10x<-6x+64` ∵
`\mathrm{Expand\:}2+2\left(-3x+31\right):\quad -6x+64`

`\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}`

`10x+6x<-6x+64+6x`

`\mathrm{Simplify}`

`16x<64`

`\mathrm{Divide\:both\:sides\:by\:}16`

`(16x)/(16)<(64)/(16)`

`x<4`

so

• Inequality notation:
  `x<4\:`

• Interval Notation:
  `\left(-\infty \:,\:4\right)`

Therefore,

`10x<2+2\left(-3x+31\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<4\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:4\right)\end{bmatrix}`

The graph of the solution set on the number line is also attached below.