Solve the following inequality. Graph the solution set and write it in interval notation

Question

8x<7x+5

Answer 1

8x<7x+5

 

Solving for x, 1st subtract 7x from both sides

 

8x-7x < 5

 

x < 5

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This is your inequality.

In interval notation this is every number less than 5

heading to negative infinity so

(-∞,5) 

The parenthesis ) on both end means that the endpoint

is not actually included in the interval.  Since you never

actually reach infinity that value is always put with a

parenthesis instead of a bracket.  If your inequality was:

x≤5 your interval notation would be (-∞,5] with the ]

indicating the 5 was included in the interval.

********************************************

As for graphing... Is your graph on a number line or a

Cartesian plane with x and y axes?

 

For a number line:

 

<-----------0--------------

                  5

 

Darken the ray to the left of the 5. The open circle at x=5

indicates the point 5 is not included.

 

To graph x<5 on a Cartesian plane you simply draw a

vertical dashed line at x=5 and shade the area to the left

of that line.

            

             y           x=5

             ∧           ∧

             |            |

             |            |

             |            |

<--------|-|-|-|-|-|--------------->x

             |            |

             |            |

             |            |

             ∨           ∨  

Answer 2

Hi Rachel,

 

To solve this equation, you would need to get all of the x terms on one side. What is the inequality generated when 8x and 7x are on the same side? 

 

To graph the solution set, you would need to draw a line for the inequality on the x-y plane and shade the portion of the plane that makes the inequality true. 

 

In interval notation, you would draw a horizontal line with two arrows at each end and make a tick mark for the value you acquired in the inequality. You would then draw a left ray from the tick mark if x is less than the value. If x is greater than the value, you would draw a right ray from the tick mark. Since the equation is purely an inequality, would there be a closed circle or open circle at the tick mark?