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Q9.

Expert-verified

Pre-algebra

Found in: Page 140

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Solve the inequality. Graph and check your solution.

$x + 4 < 3$

The solution for the inequality is $x < - 1$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step -1 - Apply the concept of Linear inequalities

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Side to maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the value of n by solving the inequality

Since, the equality is $x + 4 < 3$ .

Here, to simplify this inequality, subtract $- 4$ to both side on the above

$\begin{array}{l} x + 4 < 3 \\ x + 4 - 4 < 3 - 4 \\ x < - 1 \end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x < - 1$

So, this expression means that the value of x should be smaller than $- 1$ .

So, Put $- 2, - 3, - 4, - 5 . . . . . . . s o o n$ in $x + 4 < 3$ to check whether the inequality hold or not

Put $x = - 2$ in inequality,

$\begin{array}{l} x + 4 < 3 \\ - 2 + 4 < 3 \\ 2 < 3 \end{array}$

It holds the equation

Again, put $x = - 3$ in equality

$\begin{array}{l} x + 4 < 3 \\ - 3 + 4 < 3 \\ 1 < 3 \end{array}$

It also holds the inequality.

So, the expression $x < - 1$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x < - 1$ to get the proper graphical representation to know the points.

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