1. solve using multipication principle
-3a<-15
2. solve the equation if it an identity(all real numbers) or a contradiction ( no solution) so state
5x+6+6x=10x+6+y
-3a<-15
-3=-15
________
-3
=5
To solve the equation -3a < -15 using the multiplication principle, we need to isolate the variable "a" on one side of the inequality sign. Here are the steps you can follow:
Step 1: Divide both sides of the inequality by -3. Remember that when you divide an inequality by a negative number, the direction of the inequality sign flips.
-3a / -3 > -15 / -3
This simplifies to:
a > 5
So, the solution to the inequality -3a < -15 is a > 5.
Now let's move on to the next question:
To determine whether the equation 5x + 6 + 6x = 10x + 6 + y is an identity (for all real numbers) or a contradiction (no solution), we need to simplify it and compare the coefficients of "x" and the constant terms.
Let's start by combining like terms on both sides of the equation:
11x + 6 = 10x + y + 6
Next, we can subtract 10x from both sides to collect the x terms:
11x - 10x + 6 = y + 6
This simplifies to:
x + 6 = y + 6
Now, subtract 6 from both sides of the equation:
x = y
Since the coefficient of "x" and the constant term on both sides of the equation are the same, we can conclude that every value of "y" would have a corresponding solution for "x". Therefore, the equation is an identity, meaning it holds true for all real numbers.
Hence, the equation 5x + 6 + 6x = 10x + 6 + y is an identity for all real numbers.