Question

Consider the inequality x+3/6 ≤ x/4 +1 Which value of `x` is a solution to the inequality? Explain or show how you found your answer.

A. x= -10
B. x= -6
C. x= 6
D. x= 10

Answer 1

The inequality x+3/6 ≤ x/4 +1 simplifies to x ≥ -6. Options B, C, and D are correct as they all represent values of x that satisfy x ≥ -6.

Step-by-step explanation:

To solve the inequality x+3/6 ≤ x/4 +1, we first clear fractions by finding a common denominator. In this case, the common denominator for 6 and 4 is 12. We need to multiply both sides of the inequality by 12 to eliminate the fractions and simplify the inequality:

• 12 * (x+3)/6 ≤ 12 * (x/4 +1)
• 2 * (x+3) ≤ 3 * x + 12
• 2x + 6 ≤ 3x + 12

Next, we isolate the variable on one side:

• 6 - 12 ≤ 3x - 2x
• -6 ≤ x

Therefore, any x ≥ -6 is a solution to the inequality.

Now, we check each of the provided options against the inequality:

• A. x= -10 is incorrect because -10 is not greater than or equal to -6.
• B. x= -6 is correct because -6 is equal to -6, satisfying the inequality.
• C. x= 6 is also correct because 6 is greater than -6.
• D. x= 10 is also correct because 10 is greater than -6.

The correct selections are B, C, and D, since x ≥ -6.