To solve the inequality 24 < 2x + 5x + 5, we first combine like terms on the right side. The terms 2x and 5x can be combined:
2x + 5x = 7x
Now the inequality looks like this:
24 < 7x + 5
Next, we want to isolate the term with x. To do that, we subtract 5 from both sides:
24 – 5 < 7x
This simplifies to:
19 < 7x
Now, we divide both sides by 7 to solve for x: (Note: since 7 is positive, the inequality sign does not change.)
19/7 < x
Which can also be expressed as:
x > 19/7
To represent this in decimal form, we can calculate 19 divided by 7, which gives us approximately 2.714285714285714. So, the solution to the inequality is:
x > 2.71