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Solve the inequality. Explain all the steps and identify the properties used 3a - 4 <5

3a - 4 < 5

Add 4 to both sides:
3a < 9

Divide both sides by 3:
a < 3

The inequality is now solved.

The properties used were addition and division.

Did you know?

Did you know that solving inequalities involves finding the range of values that make the statement true? Let's take a look at an example: 3a - 4 < 5. To solve this inequality, we want to isolate the variable 'a' on one side. Step 1: Add 4 to both sides of the inequality: 3a - 4 + 4 < 5 + 4. This step uses the Property of Addition, which states that you can add the same number to both sides of an inequality without changing its direction. Step 2: Simplify both sides of the inequality: 3a + 0 < 9. Adding 4 and 5 gives us 9, and any number plus 0 is equal to itself. Step 3: Remove the 0 on the left side of the inequality: 3a < 9. Since any number multiplied by 1 is equal to itself, we can also write this as 1 * 3a < 9. Step 4: Divide both sides of the inequality by 3: (1 * 3a) / 3 < 9 / 3. This step uses the Property of Division, which states that you can divide both sides of an inequality by the same positive number without changing its direction. Step 5: Simplify both sides of the inequality: 3a / 3 < 3. Dividing 3a by 3 gives us a, and 9 divided by 3 is 3. Step 6: The final solution is a < 3, which means the values of 'a' that make the inequality true are less than 3. This inequality can also be represented as (-∞, 3), using interval notation.