Mathematics
Grade 7
15 min
Inequalities with decimal division
Inequalities with decimal division
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1
Introduction & Learning Objectives
Learning Objectives
Solve one-step inequalities involving division by a positive decimal.
Solve one-step inequalities involving division by a negative decimal.
Correctly apply the rule of reversing the inequality symbol when multiplying or dividing by a negative number.
Represent the solution set of an inequality on a number line.
Translate a real-world scenario into an inequality with decimal division.
Verify the solution to an inequality by substituting a test value.
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This tutorial will teach you how to solve inequalities when a variable is divided by a decimal. This skill is like a superpower for making smart decisions, especially wh...
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Key Concepts & Vocabulary
TermDefinitionExample
InequalityA mathematical statement that compares two values that are not necessarily equal, using symbols like < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).x / 1.2 > 5
DecimalA number that uses a decimal point to separate the whole number part from the fractional part.3.75, 0.5, -2.1
VariableA symbol, usually a letter, that represents an unknown number or a set of numbers.The letter 'y' in the inequality y / -0.8 < 10.
Solution SetThe complete set of all numbers that make an inequality true.For x > 2.5, the solution set includes 2.6, 3, 10.5, and any number greater than 2.5.
Inverse OperationThe operation that reverses the effect of another operation. Multiplication is the inverse operation of di...
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Core Formulas
Multiplication/Division Property of Inequality (Positive Number)
If a < b and c is positive (c > 0), then a * c < b * c and a / c < b / c.
When you multiply or divide both sides of an inequality by a POSITIVE decimal, the inequality symbol stays the same.
Multiplication/Division Property of Inequality (Negative Number)
If a < b and c is negative (c < 0), then a * c > b * c and a / c > b / c.
This is the most important rule! When you multiply or divide both sides of an inequality by a NEGATIVE decimal, you MUST FLIP (or reverse) the inequality symbol.
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Challenging
A water tank's total capacity, `c`, in liters, drains at a constant rate over 6.5 hours. To ensure the foundation does not flood, the average drainage rate must be less than 80.2 liters per hour. What is the maximum capacity the tank can hold to meet this condition?
A.The capacity must be less than 521.3 liters.
B.The capacity must be greater than 521.3 liters.
C.The capacity must be less than 12.34 liters.
D.The capacity must be greater than 12.34 liters.
Challenging
Which integer is a solution to BOTH `x / 1.5 > 6` AND `x / -0.5 < -22`?
A.9
B.10
C.11
D.12
Challenging
A number line shows an open circle at -7.5 and shading to the left. Which of the following inequalities has this solution set?
A.x / 1.5 < -5
B.x / -1.5 < 5
C.x / 5 > -1.5
D.x / -5 < -1.5
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