Math  /  Algebra

Questionlowing inequality algebraically. x7>8|x-7|>8
Attempt 1 out of 2

Studdy Solution

STEP 1

1. The inequality involves an absolute value expression.
2. Absolute value inequalities can be split into two separate inequalities.

STEP 2

1. Understand the nature of the absolute value inequality.
2. Split the inequality into two separate inequalities.
3. Solve each inequality separately.
4. Combine the solutions.

STEP 3

The inequality x7>8 |x - 7| > 8 means that the distance between x x and 7 is greater than 8. This can be interpreted in two ways: x7>8 x - 7 > 8 or x7<8 x - 7 < -8 .

STEP 4

Split the absolute value inequality into two separate inequalities:
1. x7>8 x - 7 > 8
2. x7<8 x - 7 < -8

STEP 5

Solve the first inequality x7>8 x - 7 > 8 :
Add 7 to both sides:
x7>8 x - 7 > 8 x>8+7 x > 8 + 7 x>15 x > 15

STEP 6

Solve the second inequality x7<8 x - 7 < -8 :
Add 7 to both sides:
x7<8 x - 7 < -8 x<8+7 x < -8 + 7 x<1 x < -1

STEP 7

Combine the solutions from both inequalities. The solution to the inequality x7>8 |x - 7| > 8 is:
x>15orx<1 x > 15 \quad \text{or} \quad x < -1
This means x x is in the intervals (,1)(15,) (-\infty, -1) \cup (15, \infty) .
The solution to the inequality is:
x(,1)(15,) x \in (-\infty, -1) \cup (15, \infty)

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