Solve the inequality: 3(x+1) < 5(x+2) = 15?
The question was not written correctly.
An inequality 3 ( x + 1 ) < 5 ( x + 2) can be solved:
3 ∙ x + 3 ∙ 1 < 5 ∙ x + 5 ∙ 2
3 x + 3 < 5 x + 10
3 x - 5 x < 10 - 3
- 2 x < 7
Divide both sides by - 2 and change the direction.
x > - 7 / 2
I do not know what 3 ( x + 1 ) < 5 ( x + 2 ) = 15 mean.
15 is certainly greater than - 7 / 2.
To solve the inequality 3(x+1) < 5(x+2), we will go through the steps one by one.
Step 1: Distribute the coefficients:
3x + 3 < 5x + 10
Step 2: Simplify the equation:
3x - 5x < 10 - 3
-2x < 7
Step 3: Divide through by -2. Remember, when you divide or multiply an inequality by a negative number, you must reverse the inequality sign.
(-2x) / -2 > 7 / -2
x > -7/2
So the solution to the inequality 3(x+1) < 5(x+2) is x > -7/2.
To solve the inequality 3(x+1) < 5(x+2), we need to simplify and isolate the variable x. Let's start by distributing the numbers on both sides of the inequality:
3(x+1) < 5(x+2)
3x + 3 < 5x + 10
Now, let's group the x terms on one side and the constant terms on the other side by subtracting 3x from both sides:
3x - 3x + 3 < 5x - 3x + 10
3 < 2x + 10
Next, we isolate the variable x by subtracting 10 from both sides:
3 - 10 < 2x + 10 - 10
-7 < 2x
Finally, to solve for x, we divide both sides by 2:
-7/2 < x
So, the solution to the inequality 3(x+1) < 5(x+2) is x > -7/2.