Question

Fill in values for a and b so that each statement is true for the inequality ax+4≤3x+b

When a=5a=5 and b=7b=7, x≤3x≤3.
When a=0a=0 and b=4b=4, the solution of the inequality is all real numbers.
When a=2a=2 and b=10b=10, the inequality has no solution.

A) a=5,b=7;a=0,b=4;a=2,b=10
B) a=5,b=7;a=2,b=10;a=0,b=4
C) a=0,b=4;a=5,b=7;a=2,b=10a=0,
D) a=2,b=10;a=5,b=7;a=0,b=4

Answer 1

The correct values for a and b in the inequality ax+4≤3x+b are a=5, b=7; a=2, b=10; and a=0, b=4.Based on these results, the correct values for a and b are a=5, b=7; a=2, b=10; and a=0, b=4

Step-by-step explanation:

The correct values for a and b are a=5 and b=7, a=2 and b=10, and a=0 and b=4.

To find the correct values, we need to analyze each statement and solve for x:

1. For a=5 and b=7, the inequality is 5x+4≤3x+7.
2. By simplifying the equation, we get 2x≤3, which means x≤1.5.
3. Hence, x≤3 is true.
4. For a=0 and b=4, the inequality is 0x+4≤3x+4.
5. By simplifying the equation, we get 4≤3x+4.
6. The inequality holds true for all real numbers of x, which means the solution is all real numbers.
7. For a=2 and b=10, the inequality is 2x+4≤3x+10.
8. By simplifying the equation, we get x≥6, which means x cannot be less than 6.
9. Therefore, there is no solution.

Based on these results, the correct values for a and b are a=5, b=7; a=2, b=10; and a=0, b=4.