91Ó°ÊÓ

Open-Ended Write an absolute value inequality for which every real number is a solution. Write an absolute value inequality that has no solution.

Write an absolute value inequality and a compound inequality for each length \(x\) with the given tolerance. a length of 36.80 \(\mathrm{mm}\) with a tolerance of 0.05 \(\mathrm{mm}\)

Match the property name with the appropriate equation. Multiplication by \(-1\) $$ \begin{array}{l}{\text { A. } 2(s-t)=2 s-2 t} \\ {\text { B. }-(a-b)=(-1)(a-b)} \\ {\text { C. }(7-y) \div(2 y)=\frac{7-y}{2 y}} \\\ {\text { D. }-[-(x-10)]=x-10} \\ {\text { E. }-(2 t-10)=11-2 t} \\ {\text { F. }-11=2 t+(-11)} \\ {\text { H. }-[3+(-y)]=-3+[-(-y)]} \\ {\text { I. }-\left(4 z^{2}\right)=4\left(-z^{2}\right)}\end{array} $$

Write an absolute value inequality and a compound inequality for each length \(x\) with the given tolerance. a length of 9.55 \(\mathrm{mm}\) with a tolerance of 0.02 \(\mathrm{mm}\)

Justifying Steps Name the property used in each step of simplification. $$ \begin{aligned}(3 x+y)+x &=3 x+(y+x) \\ &=3 x+(x+y) \\ &=(3 x+x)+y \\ &=(3 x+1 x)+y \\ &=(3+1) x+y \\ &=4 x+y \end{aligned} $$

Justifying Steps Name the property used in each step of simplification. $$ \begin{aligned} 2(5+x)+4(5+x) &=(2+4)(5+x) \\ &=6(5+x) \\ &=30+6 x \end{aligned} $$

Solve \(3|2 x-4|+5<41\) . Justify each step of your solution.

Which expression has the greatest value for \(x=-4\) and \(y=5 ?\) $$ \begin{array}{llll}{\text { A. }-3 x y} & {\text { B. } 3 x y} & {\text { C. } x y^{2}} & {\text { D. } x^{2} y}\end{array} $$

Reasoning Show that each statement is false by finding a counterexample (an example that makes the statement false). The opposite of each natural number is a natural number.

Order the numbers from least to greatest. $$ \sqrt{\frac{1}{4}}, \sqrt{\frac{1}{16}},-\sqrt{\frac{1}{8}},-\sqrt{\frac{1}{10}} $$