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Q29.

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Algebra 1
Found in: Page 323
Algebra 1

Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801

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Short Answer

Four times a number decreased by 6 is less than -2. Define a variable, write an inequality, and solve for the number.

Let x denote the number.

The inequality is 4x6<2.

The number is less than 1 as the solution of the inequality 4x6<2 is x<1.

See the step by step solution

Step by Step Solution

Step 1. Write the addition and division property of inequalities. 

The addition property of inequalities states that if the same number is added to each side of a true inequality, the resulting inequality is also true that is:

(i) If a>b, then a+c>b+c.

(ii) If a<b, then a+c<b+c.

The division property of inequalities states that if both sides of the inequality are divided by a positive number the sign of the inequality remains the same and if both sides of the inequality are divided by a negative number then the sign of the inequality changes that is:

(i) If a>b and c is a positive number then ac>bc.

(ii) If a<b and c is a positive number then ac<bc.

(ii) If a>b and c is a negative number then ac<bc.

(iv) If a<b and c is a negative number then ac>bc.

Step 2. Define a variable and write an inequality.

It is given that Four times a number decreased by 6 is less than -2.

Let x denote the number.

Therefore, the inequality is:

4x6<2

Step 3. Solve the inequality 4x−6<−2.

The solution of the given inequality 4x6<2 is:

4x6<24x6+6<2+6 by using addition property of inequality 4x<4 4x4<44 by using division property of inequality x<1

Therefore, the solution of the inequality 4x6<2 is x<1.

Therefore, the number is less than 1.

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