Using the properties of inequality, justify both steps in solving the inequality 25m−7≤17 .(4 points)
Step 1: 25m - 7 ≤ 17
In this step, we isolate the variable by adding 7 to both sides of the inequality.
25m - 7 + 7 ≤ 17 + 7
25m ≤ 24
By the property of inequality, if we add the same number to both sides of an inequality, the inequality remains the same.
Step 2: 25m ≤ 24
In this step, we divide both sides of the inequality by 25.
(25m)/25 ≤ 24/25
m ≤ 24/25
By the property of inequality, if we divide both sides of an inequality by the same positive number, the inequality remains the same.
Therefore, the solution to the inequality 25m - 7 ≤ 17 is m ≤ 24/25.
To solve the inequality 25m - 7 ≤ 17, we will justify each step using the properties of inequality:
Step 1: Add 7 to both sides
25m - 7 + 7 ≤ 17 + 7
25m ≤ 24
Justification: According to the Addition Property of Inequality, you can add the same value to both sides of an inequality without changing the direction of the inequality sign.
Step 2: Divide both sides by 25
(1/25) * 25m ≤ (1/25) * 24
m ≤ 24/25
Justification: According to the Division Property of Inequality, if you divide both sides of an inequality by a positive number, the direction of the inequality sign remains the same.
Therefore, the solution to the inequality is m ≤ 24/25.
To solve the inequality 25m - 7 ≤ 17, we will justify both steps using the properties of inequality:
Step 1: Isolate the variable term.
25m - 7 ≤ 17
To isolate the variable term, we need to get rid of the constant term (-7) on the left side of the inequality. We can do this by adding 7 to both sides of the inequality:
25m - 7 + 7 ≤ 17 + 7
25m ≤ 24
Justification:
According to the addition property of inequality, we can add the same number to both sides of an inequality without changing the inequality sign. Therefore, adding 7 to both sides is a valid step.
Step 2: Solve for the variable.
25m ≤ 24
Next, we need to solve for the variable m. In this case, we need to isolate m by dividing both sides of the inequality by 25:
(25m)/25 ≤ 24/25
m ≤ 24/25
Justification:
According to the division property of inequality, we can divide both sides of an inequality by the same positive number without changing the inequality sign. Therefore, dividing both sides by 25 is a valid step.
So, the solution to the inequality 25m - 7 ≤ 17 is m ≤ 24/25.