Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - Concept Byte - Modeling Multi-Step Inequalities - Page 185: 2


$6 \leq 4x + 2$ $1 \leq x$

Work Step by Step

Each side of the diagram represents one side of the equation. The bar separating the two sides represents the inequality sign. The left side of the equation is 6. Each yellow tile represents 1, so 6 is represented by 6 yellow tiles. Green tiles represent the variable, such as x. The right side of the diagram includes four green tiles since the coefficient of x is 4. The right side will also include 2 yellow tiles, representing the 2 on the right side of the equation. The steps to solve the equation algebraically mimic the steps using the tiles. $6 \leq4x+2$ (starting inequality) $6 (-2) \leq 4x+2 (-2)$ (subtracting two from both sides, remove the zero pair) $4 \leq 4x$ (divide both sides by 4) $\frac{4}{4} \leq \frac{4x}{4}$ (divide, remove duplicate groups) $ 1 \leq x$
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