Linear inequality, 2x+6 < 5(x-3)
2x+6 < 5(x-3) distribute 5 into x-3
2x+6 < 5x-15 move all x to one side
6 < 5x-15-2x simplify
6 < 3x-15 move 15 to other side
6+15 < 3x simplify
21 < 3x get x alone by dividing 3 on both sides
21/3 < 3x/3 simplify
7 < x and that's how you solve it.
To solve the linear inequality 2x + 6 < 5(x - 3), you'll need to isolate the variable x on one side of the inequality sign.
Let's break down the steps to solve this inequality:
Step 1: Distribute the 5 to the terms inside the parentheses on the right side of the inequality.
2x + 6 < 5x - 15
Step 2: Simplify the equation by rearranging the terms. Move all x terms to one side of the inequality and the constant terms to the other side.
2x - 5x < -15 - 6
-3x < -21
Step 3: Divide both sides of the inequality by -3. Remember, when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.
-3x / -3 > -21 / -3
x > 7
Therefore, the solution to the inequality 2x + 6 < 5(x - 3) is x > 7.
2x + 6 < 5x -15
Add 15 and subtract 2x from both sides.
21 < 3x
Divide both sides by 3.
7 < x
Oh, linear inequalities, my favorite! Let's solve this one together.
First, let's distribute the 5 on the right side:
2x + 6 < 5x - 15
Now, let's get all the x's on one side. We can do this by subtracting 2x from both sides:
6 < 3x - 15
Next, let's get rid of the -15 on the right side. We can do this by adding 15 to both sides:
6 + 15 < 3x
Which simplifies to:
21 < 3x
Finally, let's divide both sides by 3 to solve for x:
7 < x
So, the solution to the inequality 2x + 6 < 5(x - 3) is x > 7.
Just remember, this is serious math business, no clowning around!
To solve the linear inequality 2x + 6 < 5(x - 3), you can follow these steps:
Step 1: Expand both sides of the inequality by distributing the 5 on the right side:
2x + 6 < 5x - 15
Step 2: Simplify the inequality by combining like terms:
2x + 6 < 5x - 15
Subtract 2x from both sides:
6 < 3x - 15
Step 3: Move the constant term to the right side by adding 15 to both sides:
6 + 15 < 3x - 15 + 15
21 < 3x
Step 4: Divide both sides of the inequality by 3 to isolate x:
21/3 < 3x/3
7 < x
So, the solution to the inequality is x > 7.