To solve the inequality 24 > 2x + 5x + 5, we will follow these steps:
Step 1: Combine Like Terms
First, we will combine the terms on the right side of the inequality. The terms 2x and 5x can be combined:
2x + 5x = 7x
Therefore, we rewrite the inequality as:
24 > 7x + 5
Step 2: Subtract 5 from Both Sides
Next, we will isolate the term with x. To do this, we subtract 5 from both sides of the inequality:
24 – 5 > 7x
This simplifies to:
19 > 7x
Step 3: Divide Both Sides by 7
Now, we will divide both sides of the inequality by 7 to solve for x:
19/7 > x
This can also be rewritten as:
x < 19/7
Conclusion
So, the solution to the inequality 24 > 2x + 5x + 5 is:
x < 19/7
In decimal form, this is approximately x < 2.71.
This means that any value of x that is less than 2.71 will satisfy the inequality.