Problem 9 Solve each inequality. $$-2 y&... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 3: Problem 9

Solve each inequality. $$-2 y<7$$

Short Answer

Expert verified

y > -\frac{7}{2}

Step by step solution

Divide Both Sides by -2

To isolate the variable y, we need to divide both sides of the inequality by -2. Remember that dividing by a negative number reverses the inequality sign. The inequality becomes: \[ y > -\frac{7}{2} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

algebra

Algebra is the branch of mathematics concerning the study of symbols and the rules for manipulating these symbols. It is a unifying thread of almost all mathematics and includes everything from solving elementary equations to studying abstractions. When solving algebraic expressions and inequalities, remember these key steps:

Identify the terms and variables.
Combine like terms.
Isolate the variable.

For example, in the inequality $-2y < 7$:

The variable is $y$.
To isolate $y$, we need to perform operations that move terms involving $y$ to one side of the inequality and constants to the other.

Understanding these basics will help you perform well in algebra.

inequalities

Inequalities express a relationship in which one value is not equal to another. They are similar to equations but use symbols like $ < , > , \leq ,\geq $. Key points when dealing with inequalities:

Just like equations, you can add, subtract, multiply, or divide both sides of an inequality by the same number.
One crucial difference: If you multiply or divide by a negative number, you must reverse the inequality sign.

If we look at $-2y < 7$ and divide both sides of the inequality by $-2$:

The inequality sign changes direction from $<$ to $> $.
This gives the new inequality: $ y > - \frac{7}{2}$.

It鈥檚 important to grasp this rule for solving inequalities to avoid mistakes.

negative numbers division

Dividing by negative numbers can be tricky, especially in inequalities. The key point is the reversal of the inequality sign. Let鈥檚 break it down:

When you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
For example, in $-2y < 7$, dividing both sides by $-2$ changes the inequality sign from $<$ to $> $.
The result is $y > - \frac{7}{2} $, indicating that \y\ can be any number greater than \-3.5\.

This rule is essential because it is different from the rules for equations. Always double-check your work to make sure you're following the correct steps.

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91影视

Solve each inequality. $$-2 y<7$$

Short Answer

Step by step solution

Divide Both Sides by -2

Key Concepts

algebra

inequalities

negative numbers division

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