standard_description: Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
- The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
- The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
- 10 can be thought of as a bundle of ten ones — called a “ten.”
problem_activity: Problem 1
Consider the equation
$${ {|x|=5}}$$
.
This can be thought of as a system of equations, where
$${f(x)=\left | x \right |}$$
$${{g(x)}=5}$$
and
$${f(x)={g(x)}}$$
Graph
$${f(x) }$$
and
$${g(x)}$$
in the coordinate plane. Based on the graph, what are the solutions to
$${|x|=5}$$
?
Problem 2
For each absolute value equation below, answer the questions that follow.
$${|x|=-4}$$
$${ |x|=0}$$
$${ |x|=4}$$
How many solutions are there for
$$x$$
in each equation?
Thinking of each equation as two equal functions (similar to Anchor Problem #1), what does each one look like in the coordinate plane? Where do you see the solution(s)?
Problem 3
Solve each absolute value equation algebraically and verify the solution graphically.
$${|x+2|=8}$$
$${|x|+2=8}$$
$${|x+2|+1=0}$$


aligns: no