Question

What is the solution to the compound inequality?

Answer 1

The solution to the given compound Inequality is: x ≥ -31/15

What is the solution to the compound Inequality?

The compound Inequality is given as:

7x + ³/₄ ≥ 13

⁵/₂x - ¹/₃ ≥ -¹¹/₂

Let us solve the first inequality:

Multiply through by 4 to get:

28x + 3 ≥ 52

Subtract 3 from both sides to get:

28x ≥ 49

Divide both sides by 28 to get:

x ≥ ⁷/₄

Similarly, solving the second inequality, we have:

⁵/₂x - ¹/₃ ≥ -¹¹/₂

Multiply through by 6 to get:

15x - 2 ≥ -33

Add 2 to both sides to get:

15x ≥ -31

divide both sides by 15 to get:

x ≥ -31/15

Thus, the combined solution to the compound Inequality is:

x ≥ -31/15

Answer 2

`7x+(3)/(4)\geq13|\cdot4\\ 28x+3\geq52\\ 28x\geq49\\ x\geq(49)/(28)\\x\geq(7)/(4)\\\\ (5)/(2)x-(1)/(3)\geq-(11)/(2)|\cdot6\\ 15x-2\geq-33\\ 15x\geq-31\\ x\geq-(31)/(15)\\\\ x\geq-(31)/(15) \vee x\geq(7)/(4)\\ \boxed{x\geq-(31)/(15)}`