What is the second step for solving the innequality for x? 3 (x - 5) - 4x > 9
The second step for solving the inequality 3(x - 5) - 4x > 9 is to simplify the expression.
Starting from the left side of the inequality, distribute the 3 to the terms inside the parentheses:
3x - 15 - 4x > 9
Combine like terms:
-x - 15 > 9
To solve the inequality 3(x - 5) - 4x > 9, the second step is to simplify the left side of the inequality by applying the distributive property and combining like terms.
First, distribute the 3 to both terms inside the parentheses:
3(x - 5) = 3x - 15
Now, rewrite the inequality with the simplified left side:
3x - 15 - 4x > 9
Next, combine the x terms on the left side:
(3x - 4x) - 15 > 9
-x - 15 > 9
This is the result after the second step in solving the inequality.
To solve the inequality 3(x - 5) - 4x > 9 for x, we need to simplify and isolate the variable x. Here's the step-by-step process:
1. Distribute the 3 across the parentheses: 3x - 15 - 4x > 9.
This gives us: -x - 15 > 9.
2. Combine like terms: -x - 15 > 9.
Combine the x terms, which gives us: -5x - 15 > 9.
The second step for solving this inequality is to isolate the variable x by getting rid of the constant term. In this case, -15 is the constant term. To do this, we will add 15 to both sides of the inequality:
-5x - 15 + 15 > 9 + 15.
This simplifies to: -5x > 24.
Now we have -5x > 24. The next step is to isolate the variable x by dividing both sides of the inequality by -5. However, we need to be cautious when dividing by a negative number. Dividing by a negative number flips the inequality sign. So, the second step should be:
3. Divide both sides by -5, and reverse the inequality sign:
-5x / -5 < 24 / -5.
The inequality becomes: x < -24/5.
Thus, the second step for solving the given inequality 3(x - 5) - 4x > 9 is to divide both sides by -5 and reverse the inequality sign, resulting in x < -24/5 as the solution.