Solving multi-step linear inequalities

Linear Inequalities are more like Linear Equations that have >, <, \geq or \leq instead of an equal sign. Say for example you have the equation x>4 then this means the solution of this inequality is any number that is more than 4. The graph on the number line would then be a line with an open circle to exclude 4 but include all points that are found beyond 4 like 4.1 or 4.01.

In graphing the solution set, we can either use an open circle which would indicate that the point is not included like in the case of the example we have earlier or a closed circle which means that the point is included if you see \geq or \leq in the equation.

In solving for the values of x, we are just going to treat the inequality as a linear equation. We discussed all about linear equations and how to solve them in chapters on linear relations and solving linear equations. So, it would really be useful to review the concepts we learned there. It would also be very handy to review the basic concepts we have learned on linear Relations and linear equations, in earlier grade.

This chapter has three parts and each part would focus on specific topics about Linear Equalities. In the first part, we will be looking at how to graph and express linear equalities. This is where we will get to learn how to identify the boundary points or the critical points which are basically the values of x.

In the second part of this chapter we will be learning all about solving one step linear inequalities. Again, using the concepts we learned in Grade 8 about Linear Relations and Linear Equations, we will be able to solve one step inequalities like how we solved one step linear equations.

Lastly, in the third part of this chapter we will be looking at solving multi-step inequalities by applying all of the concepts we learn in solving one-step linear equations.

Solving multi-step linear inequalities

We learn how to solve multi-step linear inequalities in this lesson. Besides typical math questions, we are going to see word problems related to multi-step linear inequalities and money.


  • 1.
    • b)
      12.47.2x10x1512.4 - 7.2x \le 10x - 15
  • 2.
    Bob works for car dealer A which offers him a base rate of $800 and $15 for every car he sells. Tom works for car dealer B which gives him a base rate of $700 and $20 for each car he sells. If they sold the same number of cars last month, and Tom earned more than Bob. What is the minimum number of cars Tom sold last month?
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Solving multi-step linear inequalities

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