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Let's denote the unknown number as \( x \).
The problem states that "five more than four times a number is less than 25." This can be translated into the following inequality:
\[ 4x + 5 < 25 \]
Now, let's solve for \( x \):
1. Subtract 5 from both sides of the inequality to isolate the term with \( x \) on one side:
\[ 4x + 5 - 5 < 25 - 5 \]
\[ 4x < 20 \]
2. Divide both sides of the inequality by 4 to solve for \( x \):
\[ \frac{4x}{4} < \frac{20}{4} \]
\[ x < 5 \]
So the possible values of the number \( x \) are all real numbers less than 5.
uuuhhh can you tell me what this is: \[ \frac{4x}{4} < \frac{20}{4} \]
Certainly! The expression \[ \frac{4x}{4} < \frac{20}{4} \] is a step in solving the inequality we're working on. What we're doing here is dividing both sides of the inequality by 4 to isolate the variable \( x \).
On the left side of the inequality:
\[ \frac{4x}{4} \]
Since \( 4x \) is being divided by 4, these 4s will cancel each other out because dividing by the same number effectively undoes the multiplication by that number. This simplifies to just \( x \).
On the right side of the inequality:
\[ \frac{20}{4} \]
We're simply calculating the result of dividing 20 by 4, which gives us 5.
After performing these operations, our inequality simplifies to:
\[ x < 5 \]
This tells us that the variable \( x \) should be any real number less than 5 to satisfy the original problem's conditions.
no in number form, cuz i cant tell by script
Of course! The expression in standard numerical form is:
x < 5
The inequality sign "<" indicates that x is strictly less than 5. Therefore, any number that is less than 5 (but not equal to 5) is a solution to the inequality.
can you tell me this in number form please: \[ \frac{4x}{4} < \frac{20}{4} \]
Certainly! The expression in standard numerical form without the LaTeX formatting is:
4x / 4 < 20 / 4
Dividing both sides by 4 gives us:
x < 5
This means that x must be less than 5 to satisfy the inequality.