Question

Select all possible solutions to the following inequality:
4(​2x ​+​ 7) ​<​ ​2(21 – 3x)

Answer 1

To solve the inequality 4(2x + 7) < 2(21 – 3x), distribute the coefficients, combine like terms, and isolate x by dividing both sides by 14.

Step-by-step explanation:

To solve the inequality 4(2x + 7) < 2(21 – 3x), we can start by distributing the coefficients:

• 8x + 28 < 42 – 6x

Next, we can combine like terms:

• 8x + 6x < 42 – 28
• 14x < 14

Finally, we can divide both sides by 14 to isolate x:

• x < 1

Therefore, the possible solutions to the inequality 4(2x + 7) < 2(21 – 3x) are all values of x that are less than 1.

Answer 2

x < 1

Step-by-step explanation:

given the inequality

4(2x + 7) < 2(21 - 3x) ← distribute parenthesis on both sides

8x + 28 < 42 - 6x ( add 6x to both sides )

14x + 28 < 42 ( subtract 28 from both sides )

14x < 14 ( divide both sides by 14 )

x < 1