Algebra 1

Published by Prentice Hall

Chapter 3 - Solving Inequalities - 3-6 Compound Inequalities - Practice and Problem-Solving Exercises - Page 205: 40

Answer

$y\gt9.5$ or $y\lt-6\frac{2}{3}$

Work Step by Step

$\frac{4y+2}{5}-5\gt3\longrightarrow$ using the addition property of inequality, add 5 to each side $\frac{4y+2}{5}-5+5\gt3+5\longrightarrow$ add $\frac{4y+2}{5}\gt8\longrightarrow$ using the multiplication property of equality, multiply each side by 5 $\frac{4y+2}{5}\times5\gt8\times5\longrightarrow$ multiply $4y+2\gt40\longrightarrow$ using the subtraction property of inequality, subtract 2 from each side $4y+2-2\gt40-2\longrightarrow$ subtract $4y\gt38\longrightarrow$ using the division property of inequality, divide each side by 4 $4y\div4\gt38\div4\longrightarrow$ divide $y\gt9.5$ OR $\frac{4-3y}{6}\gt4\longrightarrow$ using the multiplication property of inequality, multiply each side by 6 $\frac{4-3y}{6}\times6\gt4\times6\longrightarrow$ multiply $4-3y\gt24\longrightarrow$ using the subtraction property of inequality, subtract 4 from each side $4-3y-4\gt24-4\longrightarrow$ subtract $-3y\gt20\longrightarrow$ using the division property of inequality, divide each side by -3; reverse the inequality sign $-3y\div-3\lt20\div-3\longrightarrow$ divide $y\lt-6\frac{2}{3}$

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