Solve inequalities using addition and subtraction (Advanced)

Learning Objectives Solve one-step addition inequalities involving terms in scientific notation. Solve one-step subtraction inequalities involving terms in scientific notation. Isolate a variable in an inequality by applying the Addition and Subtraction Properties of Inequality to numbers in scientific notation. Manipulate terms in scientific notation to have common exponents before solving an inequality. Express the solution set of an inequality involving large or small numbers in proper scientific notation. Verify the solution to an inequality by substituting a value from the solution set. How much more data can a new supercomputer hold compared to an old one? 💻 We can use inequalities with scientific notation to compare enormous quantities and find the answer! In this t...

TermDefinitionExample Scientific NotationA method for expressing very large or very small numbers as a product of a coefficient and a power of 10, in the form a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer.The number 5,400,000 is written as 5.4 × 10⁶. InequalityA mathematical statement that asserts that two values are not equal, using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).x + 5 > 12 Addition Property of InequalityAdding the same number to both sides of an inequality does not change the truth of the inequality statement.If x - 3 < 7, then adding 3 to both sides gives x < 10. Subtraction Property of InequalitySubtracting the same number from both sides of an inequality does not change the truth of the i...

Addition Property of Inequality If a < b, then a + c < b + c Use this rule to isolate a variable when a value is being subtracted from it. Add the value to both sides of the inequality. Subtraction Property of Inequality If a > b, then a - c > b - c Use this rule to isolate a variable when a value is being added to it. Subtract the value from both sides of the inequality. Addition/Subtraction in Scientific Notation (a \times 10^n) \pm (b \times 10^n) = (a \pm b) \times 10^n To add or subtract numbers in scientific notation, their exponents (n) must be identical. If they are, simply add or subtract the coefficients (a and b) and keep the common power of 10.