5 (x + 3) + 6 < 3 (x - 2) + 5
Help sove with all the steps
5 (x + 3) + 6 < 3 (x - 2) + 5
5x + 15 + 6 < 3x - 6 + 5
2x < -21 -1
2x < -22
x > -11
Though the x value is correct, since you are not dividing -22 with a negative sign ie -2, you cannot flip the sign. To be clear the sign should remain the same as
x<-11
To solve the inequality 5(x + 3) + 6 < 3(x - 2) + 5, follow these steps:
Step 1: Simplify both sides of the inequality:
Distribute 5 and 3 on their respective terms:
5x + 15 + 6 < 3x - 6 + 5
Combine like terms:
5x + 21 < 3x - 1
Step 2: Move all the variables (terms with x) to one side of the inequality:
Subtract 3x from both sides:
5x - 3x + 21 < -1
Combine like terms:
2x + 21 < -1
Step 3: Move the constant term to the other side:
Subtract 21 from both sides:
2x + 21 - 21 < -1 - 21
Simplify:
2x < -22
Step 4: Solve for x by dividing both sides by the coefficient of x, which is 2:
(2x)/2 < (-22)/2
Simplify:
x < -11
So, the solution to the inequality is x < -11.