10x >2(7x+3)+2
Please help me solve this and show your work thanks
To solve the inequality 10x > 2(7x + 3) + 2, we need to simplify both sides of the equation and isolate the variable x.
Step 1:
Expand the expression on the right side of the inequality:
10x > 2(7x + 3) + 2
10x > 14x + 6 + 2
10x > 14x + 8
Step 2:
Next, we want to collect all the terms with x on one side of the inequality. To do this, we'll subtract 14x from both sides:
10x - 14x > 14x + 8 - 14x
-4x > 8
Step 3:
Now, we'll divide both sides of the inequality by -4. Pay attention to the fact that when we divide by a negative number, the inequality sign flips:
-4x/(-4) < 8/(-4)
x < -2
Step 4:
The result is x < -2. This means that any value of x less than -2 will satisfy the inequality 10x > 2(7x + 3) + 2.
In summary, the solution to the inequality 10x > 2(7x + 3) + 2 is x < -2.