Question

"Which of the following are solutions to the inequality -7x + 14 > -3x - 6? Select all that apply.

A.) -10
B.) 10
C.) -5
D.) 5
E.) -3
F.) 3
G.) 0"

Answer 1

To solve the inequality -7x + 14 > -3x - 6, we simplify it to x < 5. Thus, the solutions are the numbers less than 5, which are -10, -5, -3, and 3.

Step-by-step explanation:

The question asks us to determine which of the following numbers are solutions to the inequality -7x + 14 > -3x - 6. To find the solution, we need to follow these steps:

• First, add 3x to both sides of the inequality to get -7x + 3x + 14 > -6.
• Simplify the inequality to -4x + 14 > -6.
• Next, subtract 14 from both sides to isolate the variable term: -4x > -20.
• Divide both sides by -4, remembering to flip the inequality sign because we are dividing by a negative number. This gives us x < 5.
• Now, we test which of the provided numbers are less than 5.

Numbers that are solutions to the inequality x < 5 are: A.) -10, C.) -5, E.) -3, and F.) 3. Option B.) 10, D.) 5, and G.) 0 are not solutions because they are not less than 5.