PowerPoint created by Parsheena Berch Resource : JBHM material Pictures: Google Images

Solving Equations and Inequalities; Inverse Operations

Sometimes you not only need to know exactly how much something is but you might need to know an exact amount and anything greater than or less than that. Does this make sense? Let me explain. Say that I want to spend no more than $50 on a college blanket. What does that mean? That means that I will spend up to $50 so $50 and anything less than $50 will be an okay amount for me to spend. Our lesson today will be on inequalities such as this.

Solving Inequalities: Turn to page 142 Teacher edition pages An inequality is not the same as an equation even though there are some similarities in the way they are solved. In an equation the expressions on each side of the equal sign are always equal. An inequality compares two expressions in which the value of one side may be greater than (>), less than (<), greater than or equal to ( ≥ ), or less than or equal to ( ≤ ) to the other side. The prefix in means not so, inequality generally means not equal to.

≠ means is not equal to < means is less than ≤ means is less than or equal to > means is greater than ≥ means is greater than or equal to One way to remember the correct meaning is that the symbol points to the smaller number. Notice the difference between the ones that include equal to. They include half of the equal sign, thus the equal to.

Inequality: A mathematical sentence that compares two mathematical phrases, one of which must be algebraic.

2x > 5 two times x is greater than five 19 + y < 24 nineteen plus y is less than twenty-four a/27 ≥ 9 a divided by twenty-seven is greater than or equal to nine z – 42 ≤ 36 z minus forty-two is less than or equal to thirty-six

Write the inequality using numbers and symbols on white boards. y minus seventeen is less than or equal to eight. (y – 17 ≤ 8) The sum of a number and fifty-two is greater than sixty- one. (x + 52 > 61) A number divided by one hundred twelve is less than two. (n ÷ 112 < 2) The product of thirteen and n is greater than or equal to seventy-eight. (13n ≥ 78) Five times x is greater than or equal to sixty. (5x ≥ 60)

Solving basic inequalities is like solving equations. However, the sign will be the sign used in the inequality, so it won’t be =. The steps to solving inequalities will be similar to those used in solving equations. The solution to a simple inequality is always written with the variable, an inequality symbol, and a value. For example: If the problem is x + 2 > 5, writing the answer 3 does not tell us if x equals 3, is greater than 3, or is less than 3. The variable and inequality sign as well as the value must be written when writing solutions to inequalities. The correct solution is x > 3.

Your turn! Work the examples on page 142 Check your answers.

62 + z ≥ 139 x – 29 ≤ 48 y ≤ 93 z – 203 > y < 108 t ÷ 16 ≥ 9 24 n > 144 y/225 ≤ 3 9y < 63

Closure: Don’t forget that your homework is due tomorrow. Who can tell the class how to solve an equation or an inequality?

Homework for the week: y = 573 z – 24 = 13 a ÷ 42 = 6 ? 4 = 48 x + 3 = 12 y – 2.8 = = 7 + z 2 ½ + y = 6 9a = 31.5 y/13 = 7