using the properties of inequality, justify both steps in solving the inequality 25m−7≤17

To solve the inequality \(25m - 7 \leq 17\), we will justify our steps using properties of inequality.

1. **Adding 7 to both sides**: The first step is to isolate the term with \(m\). We add 7 to both sides of the inequality:

\[
25m - 7 + 7 \leq 17 + 7
\]

This simplifies to:

\[
25m \leq 24
\]

**Justification**: Adding the same number to both sides of an inequality maintains the inequality's direction. This property ensures that if one side is less than or equal to the other, that relationship holds true after the addition.

2. **Dividing by 25**: Next, we want to solve for \(m\) by dividing both sides by 25:

\[
\frac{25m}{25} \leq \frac{24}{25}
\]

This simplifies to:

\[
m \leq \frac{24}{25}
\]

**Justification**: Dividing both sides of an inequality by a positive number (in this case, 25) also keeps the inequality's direction intact. This means if \(A \leq B\) and you divide both by a positive \(C\), the inequality remains \( \frac{A}{C} \leq \frac{B}{C}\).

Overall, we solved the inequality step by step while ensuring to maintain the inequality's direction by using properties of addition and division specific to positive numbers.

can you explain without steps pls?

Certainly! When solving the inequality \(25m - 7 \leq 17\), we want to isolate \(m\) while keeping the inequality valid.

First, we can add 7 to both sides of the inequality. This operation preserves the relationship because adding the same quantity to both sides does not change which side is greater or lesser.

Next, to solve for \(m\), we divide both sides by 25. Since 25 is a positive number, this division still keeps the inequality intact.

In summary, both steps—adding 7 and dividing by 25—are justified by the properties of inequalities: we can add or subtract the same value from both sides, and we can divide by a positive value without reversing the inequality. This leads us to the solution \(m \leq \frac{24}{25}\).

using the properties of inequality, justify both steps in solving the inequality 2/5m−7≤17

sorry i forgot to ad the fraction lol

can you explain again without steps?

Sure! In solving the inequality \(\frac{2}{5}m - 7 \leq 17\), we want to isolate the variable \(m\) while ensuring that the inequality remains true throughout the process.

Initially, we start by adding 7 to both sides of the inequality. This is valid because when we add the same number to both sides, we keep the original relationship between the two sides intact. The inequality remains valid, meaning if one side is less than or equal to the other, that relationship still holds after the addition.

Next, to isolate \(m\), we multiply both sides of the inequality by \(\frac{5}{2}\). Since \(\frac{5}{2}\) is a positive number, multiplying both sides by it does not change the direction of the inequality. This ensures that the relationship between the sides is preserved.

Thus, by adding 7 and then multiplying by \(\frac{5}{2}\), we arrive at a solution for \(m\) that satisfies the original inequality, all while adhering to the properties of inequalities that allow us to manipulate the equation correctly.