Question

Solve each inequality. Check your answer. $$-30 \leq d+(-5)$$

   Solve each inequality. Check your answer.
$$-30 \leq d+(-5)$$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 8, Problem 23

Instant Answer

Solved by Expert Will Cadelina

05/22/2020

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Step 1: We start with the inequality $-30 \leq d+(-5)$. Show more…

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Solve each inequality. Check your answer. $$-30 \leq d+(-5)$$

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Key Concepts

Linear Inequalities

Linear inequalities involve expressions where one linear expression is related to another using inequality symbols (such as <, ?, >, or ?). They represent a range or interval of possible values rather than a single solution, and the process of solving them focuses on isolating the variable through valid algebraic operations that maintain the inequality's direction.

Operations on Inequalities

Operations on inequalities involve performing algebraic manipulations, such as adding or subtracting the same quantity from both sides, to simplify the inequality and isolate the variable. It is important to remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign, a key property when solving such expressions.

Isolating the Variable

Isolating the variable in an inequality is a step-by-step process where like terms and constants are manipulated so that the variable stands alone on one side of the inequality. This process often involves adding or subtracting terms and, when necessary, multiplying or dividing by positive numbers to solve for the variable's range of values.

Verification of Solutions

Verification of solutions in inequalities involves substituting values from the solution set back into the original inequality to ensure that the solution satisfies it. This step helps confirm that the algebraic manipulations performed maintained the inequality’s validity across the derived interval.

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