Systems of Linear Equations and Inequalities 2.4 Solving Linear Inequalities Solve linear inequalities algebraically Solve linear inequalities graphically or numerically. Solve applications using linear inequalities

Solving Linear Inequalities A linear inequality in two variables can be written in one of the following forms: Where a, b, and c are real numbers and a and b are not both zero.

Solving Inequalities: Solve the following Inequalities. -6b + 10 > 40 8g - 12 ≤ 3g + 2 4x + 12 > 10 8h + 9 ≤ 10h + 1 𝒎 −𝟑 −𝟖 < 𝟏𝟎 𝒙>− 𝟏 𝟐 h ≥ 4 𝒎>−𝟓𝟒 𝒃<−𝟓 g ≤ 𝟏𝟒 𝟓

Systems as Inequalities If we consider the U-Haul and Bob’s Truck Rental, Find the distances that you can drive that will result in Bob’s being less expensive than U-Haul. U(m) = The total cost in dollars to rent a 10-foot truck from U-Haul B(m) = The total cost in dollars to rent a 10-foot truck from Bob’s Truck Rental m = The number of miles traveled in rented truck. U(m) = 19.95 + 0.79m B(m) = 24.95 + 0.75m 𝒎>𝟏𝟐𝟓

Systems as Inequalities The percentage of college Freshmen who were male and the percentage of college Freshmen who were female for various years are given in the chart. Find the equations for models of these data. Determine the years for which the number of male freshmen was greater than or equal to the number of female freshman. Let M(t) = Percentage of college freshmen who are male F(t) = Percentage of college Freshmen who are female t = Time in years since 1980

Systems as Inequalities The percentage of college Freshmen who were mal and the percentage of college Freshmen who were female for various years are given in the chart. Find the equations for models of these data. Determine the years for which the number of male freshmen was greater than or equal to the number of female freshman. Let M(t) = Percentage of college freshmen who are male F(t) = Percentage of college Freshmen who are female t = Time in years since 1980 𝑴 𝒕 =−𝟎.𝟏𝟓𝟖𝒕+𝟒𝟖.𝟔𝟒2 F(t) = 0.158t + 51.358 M(t) ≥ F(t) where t ≤ -8.59. So in 1971 and before, the percentage of freshmen who were male was greater than or equal to the percentage of freshmen who were female.

Solve Inequalities Numerically Use the table on the calculator to numerically find the solutions to the following systems of equations. 5x + 7 > 2x + 31 4x + 9 ≤ 6x - 1 -3x + 8 > x - 4 𝒙>𝟖 x ≥ 5 x < 3

Solve Inequalities Graphically Solve the following inequalities graphically. −2x + 9 ≤ 4x - 33 2.5x + 4 < 3.5x + 6 1.25x - 2 ≥ 2x - 5 𝒙 ≥ 𝟕 x > -2 x < 4