The annual expenses of a manufacturing company must satisfy the inequality that follows, where x is in millions of dollars.
2(x-5)>6(x-3)
A. Solve the inequality for x. Interpret the result.
Except for multiplying/dividing by a negative number, treat just like an equation.
First get rid of the parentheses by multiplying.
2x - 10 > 6x -18
Subtract 2x from both sides and add 18 to both sides.
You should be able to work it from there.
is it 28>4x
or -10>4x?
2(x-5)>6(x-3)
2x - 10 > 6x - 18
2x - 6x > -18+10
-4x > -8
x < 2
To solve the inequality 2(x-5) > 6(x-3) and interpret the result, we can follow these steps:
Step 1: Distribute the terms on both sides of the inequality:
2x - 10 > 6x - 18
Step 2: Combine like terms on each side of the inequality:
-10 > 4x - 18
Step 3: Move the variable term to one side and the constant term to the other side of the inequality:
4x < 18 - 10
4x < 8
Step 4: Divide both sides of the inequality by 4:
x < 2
Interpretation:
The result of the inequality x < 2 means that the annual expenses of the manufacturing company must be less than 2 million dollars in order to satisfy the given inequality. In other words, if the expenses are equal to or greater than 2 million dollars, the inequality will not hold true.