Mari is solving the inequality 4(x - 3) > 16. Her first step is 4x - 12 > 16.
Which step could be the next step? Select all that apply.
(3 points)
4x - 12 + 12 > 16 + 12
4x - 12 + 12 > 16 + 12
4x - 12 - (-12) > 16 - (-12)
4x - 12 - (-12) > 16 - (-12)
(14)(4x − 12) > 16 (1(4))
(14)(4x − 12) > 16 (1(4))
4x4 − 12 > 164
4x4 − 12 > 164
4(4x - 12) > 16(4)
The next step could be:
4x - 12 + 12 > 16 + 12
4x - 12 - (-12) > 16 - (-12)
4(4x - 12) > 16(4)
To solve the inequality 4(x - 3) > 16, Mari's first step was to distribute the 4 to both terms inside the parentheses, resulting in 4x - 12 > 16.
The next step could be to add 12 to both sides of the inequality:
4x - 12 + 12 > 16 + 12.
This step is valid because adding the same value to both sides of an inequality does not change the inequality.
Alternatively, the next step could be to subtract -12 from both sides of the inequality:
4x - 12 - (-12) > 16 - (-12).
This step is valid because subtracting a negative value is equivalent to adding its positive value.
The next step should not involve multiplying or dividing by a constant, as it would change the inequality unless both sides are multiplied or divided by a positive number. So, the following options are not correct:
(14)(4x − 12) > 16 (1(4))
4x4 − 12 > 164
4(4x - 12) > 16(4)
Remember, when solving inequalities, you need to perform the same operation on both sides while maintaining the direction of the inequality.
The correct next steps are:
1. 4x - 12 + 12 > 16 + 12
2. 4x - 12 - (-12) > 16 - (-12)
3. 4(4x - 12) > 16(4)
So, the options are:
- 4x - 12 + 12 > 16 + 12
- 4x - 12 - (-12) > 16 - (-12)
- 4(4x - 12) > 16(4)