Question

Solve the inequality. $$ 2 x+3<-1 \text { or } 3 x-5>-2 $$

   Solve the inequality.
$$
2 x+3<-1 \text { or } 3 x-5>-2
$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 6, Problem 9

Instant Answer

Solved by Expert Amy Jiang

09/02/2020

Step 1

We can do this by subtracting 3 from both sides in the first inequality and adding 5 to both sides in the second inequality. This gives us: $$ 2x < -4 \text { or } 3x > 3 $$ Show more…

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Solve the inequality. $$ 2 x+3<-1 \text { or } 3 x-5>-2 $$

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Key Concepts

Linear Inequalities

Linear inequalities are algebraic expressions that involve linear expressions on one or both sides of an inequality sign (such as <, >, ?, or ?). The process of solving them involves manipulating the inequality in a similar way to solving linear equations, while keeping in mind that multiplying or dividing by a negative number reverses the inequality sign.

Compound Inequalities with OR

When multiple inequalities are connected by the word 'or', they represent a union of solution sets. This means that any value satisfying at least one of the inequalities is considered a solution. Understanding this concept is essential for accurately combining the results of separate inequality solutions.

Algebraic Manipulation

Algebraic manipulation refers to the process of isolating the variable in an inequality by performing equivalent operations on both sides. This includes adding or subtracting terms and multiplying or dividing by constants, while being cautious of reversing the inequality when dividing or multiplying by a negative number.

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