Graph and Solve One-Step Inequalities

Solving and Graphing Inequalities (One Step)

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Inequalities

Addition and Subtraction

Inequality

• An Inequality is a mathematical sentence

• Uses symbols, such as <, ≤, >, ≥, or ≠ to compare to quantities.

  
  

Multiple Choice

What do these symbols mean? (from left to right)

• less than

• less than or equal to

• greater than

• greater than or equal to

Multiple Choice

What do these symbols mean? (from left to right)

• less than

• less than or equal to

• greater than

• greater than or equal to

Multiple Choice

What do these symbols mean? (from left to right)

• less than

• less than or equal to

• greater than

• greater than or equal to

Multiple Choice

What do these symbols mean? (from left to right)

• less than

• less than or equal to

• greater than

• greater than or equal to

Reading Inequalities

• Remember: Inequalities can be read in either direction....

• As long as you use the correct vocabulary for the symbol.

Multiple Select

Inequality

Write an inequality for the sentences below.

The sum of a number, n, and fifteen is greater than or equal

to nine.

• 15n < 9

• n - 15 > 9

• n + 15 ≥ 9

Multiple Select

Inequality

Write an inequality for the sentences below.

Three times a number, n, is less than 210.

• 3n < 210

• 3 + n > 210

• 3 - n ≥ 210

Graphing Inequalities

• Remember!!!

Solving Inequalities

• Solving one-step inequalities is much like solving one-step

  equations.

• To solve an inequality, you need to isolate the variable using the

  properties of inequalities and inverse operations.

Isolate the Variable

• To find the solution, isolate the variable x.

  
  

• Remember, it is isolated when it appears by itself on one side of the inequality.

  
  

Solving Inequalties

• Step 1: Since 6 is added to x and subtraction is the inverse of

  addition, subtract 6 from both sides to undo the addition.

Solving Inequalties

• Step 2: Decide whether or not the circle on your boundary

  should be open or closed based on the symbol used.

• You can check the computation by substituting the end point

  of 6 into the inequality for x.

• In this case, the end point is not included (open circle) since x < 6.

Multiple Choice

Solving Inequalities

Solve the following inequality.

• x≠-15

• x≠-9

Multiple Choice

Solving Inequalities

Solve the following inequality. How can we graph it?

• closed circle shade to left and right

• open circle shade to left and right

Multiple Choice

s+8 > 2

Multiple Choice

What is the solution?

• a

• b

• c

Poll

x>1.5

• a

• b

• c

• d

• e