## Algebra 1

Published by Prentice Hall

# Chapter 3 - Solving Inequalities - Pull it All Together - Page 221: Task 2

#### Answer

rectangle $x\leq24$ triangle $x\gt1$

#### Work Step by Step

The area of a rectangle is found by multiplying length times width. In the diagram, the width is 3 and the length is x. $3x\leq72\longrightarrow$ divide each side by 3 $3x\div3\leq72\div3\longrightarrow$ divide $x\leq24$ The area of a triangle is $\frac{1}{2}bh$. In the diagram, the base is 20 and the height is $x+2$. $\frac{1}{2}(20)(x+2)\gt30\longrightarrow$ multiply $10(x+2)\gt30\longrightarrow$ multiply using the distributive property $10x+20\gt30\longrightarrow$ subtract 20 from each side $10x+20-20\gt30-20\longrightarrow$ subtract $10x\gt10\longrightarrow$ divide each side by 10 $10x\div10\gt10\div10\longrightarrow$ divide $x\gt1$

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