how do I solve this problem?
-(6x+1)<-3x(4-1)+5
-6x-1<-12x+3+5 distribute
-6x-1<-12x+8 and simplify
6x<9
x<3/2
First row, the 3 should be 3x..go from there.
To solve the given problem -(6x+1)<-3x(4-1)+5, we can follow these steps:
Step 1: Simplify both sides of the inequality.
On the left side, distribute the negative sign to each term inside the parentheses:
-(6x+1) = -6x - 1
On the right side, use the distributive property to multiply -3x by each term inside the second set of parentheses:
-3x(4-1) = -3x * 4 + (-3x) * (-1) = -12x + 3x = -9x
So the inequality becomes:
-6x - 1 < -9x + 5
Step 2: Group the variable terms on one side and the constant terms on the other side.
To do this, we can move the -9x term from the right side to the left side by adding 9x to both sides:
-6x - 1 + 9x < -9x + 5 + 9x
Simplifying further, we get:
3x - 1 < 5
Step 3: Isolate the variable term.
To isolate the x-term, we can move the constant term (-1) to the right side by adding 1 to both sides:
3x - 1 + 1 < 5 + 1
Simplifying further, we get:
3x < 6
Step 4: Solve for x.
Divide both sides of the inequality by 3 to solve for x:
(3x)/3 < 6/3
Simplifying further, we get:
x < 2
Therefore, the solution to the given inequality is x < 2.