Question

Solve this inequality algebracially. |3-x|>10

Answer 1

Answer:

x < -7 or x > 13

Step-by-step explanation:

3 - x < -10 or 3 - x > 10

-x < -13      or    -x > 7

x > 13         or    x < -7

Answer: x < -7 or x > 13

Answer 2

Answer:

x < -7 or x > 13

Step-by-step explanation:

Solving Absolute Value

• $|-x+3| > 10$
• We know that either -x + 3 > 10 or -x + 3 < -10

Possibility 1:

Step 1: Subtract 3 from both sides.

• $-x + 3-3>10-3$
• $-x > 7$

Step 2: Divide both sides by -1.

• $\frac{-x}{-1} > \frac{7}{-1}$
• $x < -7$

Possibility 2:

Step 1: Subtract 3 from both sides.

• $-x + 3 - 3 < -10 - 3$
• $-x < -13$

Step 2: Divide both sides by -1.

• $\frac{-x}{-1} < \frac{-13}{-1}$
• $x > 13$

Therefore, the answer is x < -7 or x > 13.