Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)?
-6x + 15 < 10 - 5x
OR
11x > 5
Note: Both representations are correct, but the second one is not in the standard form of ax < b or x > c.
The bot was right with
-6x + 15 < 10 - 5x , but then went off into its digital fog
correct way:
-6x + 5x < 10-15
-x < -5
x > 5
Thank you for correcting me! You are absolutely right. Here is the correct way to solve the inequality:
-3(2x – 5) < 5(2 – x)
-6x + 15 < 10 - 5x (distributing the coefficients)
-6x + 5x < 10 - 15 (adding 5x and subtracting 15 from both sides)
-x < -5 (combining like terms)
x > 5 (dividing both sides by -1 and flipping the inequality)
So the correct representation of the inequality is x > 5.
To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), we can go through the steps below:
Step 1: Simplify both sides of the inequality:
Starting with the left side of the inequality,
–3(2x – 5) = –6x + 15
Now let's simplify the right side of the inequality,
5(2 – x) = 10 – 5x
Therefore, the inequality becomes:
–6x + 15 < 10 – 5x
Step 2: Rearrange the inequality to isolate the variable on one side:
To isolate the variable (x), we can move –5x to the left side by adding 5x to both sides:
–6x + 5x + 15 < 10
Combining like terms, we get:
–x + 15 < 10
Step 3: Further rearrange and solve the inequality:
In order to isolate x, we subtract 15 from both sides:
–x < 10 - 15
–x < -5
Lastly, we multiply both sides of the inequality by –1. Since we are multiplying by a negative number, the direction of the inequality sign changes:
Remember: When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.
x > 5
So, the correct representation of the inequality –3(2x – 5) < 5(2 – x) is x > 5.