1. Complete the solution of the equation It- 71 = 8. Think: "The value of the quantity t-7 can be 8 or -8." Rewrite It – 71 = 8 as t- 7 = 8 or t-7+7 =8+7 Add 7 to each side or to isolate t. or Simplify.
The absolute value is positive. −4 −2 0 2 4
The absolute value is negative. 5|x − 3| = 20
x − 3 = −4
The equation has no solution because
no value of x makes the equation true. −4 −2 0 2 4
The graph of the solutions for an
absolute value inequality using > or ≥,
or a compound inequality using or.
5|x − 3| = 20
x − 3 = 4
The graph of the solutions for an
absolute value inequality using < or ≤,
or a compound inequality using and.
|x + 10| = −9
1. Complete the solution of the equation |t − 7| = 8.
Think: “The value of the quantity t − 7 can be 8 or −8.”
Rewrite |t − 7| = 8 as t − 7 = 8 or .
t − 7 + 7 = 8 + 7 or Add 7 to each side
to isolate t.
or Simplify.
2. Tavon says that for the absolute value inequality |z| < 6, you read the inequality
as “z is less than 6 away from zero.” Marta believes you read the inequality as
“z is less than 6.” Who is correct? Explain.
3. Complete the table below for each absolute value inequality.
Inequality Solution
∣ x – 3 ∣ > 5
∣ n + 1 ∣ ≤ 7 –8 ≤ n ≤ 6
∣ d + 4 ∣ < 3
∣ f – 5 ∣ ≥ 1 f ≥ 6 or f ≤ 4
Graph
−4 −2 0 2 4 6 8 10
0 2 4 6
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