Is the following inequality always,sometimes,never,true,2(8x-4)-2 x<14x+12 thank you
the answer is b (always true) just took the quiz
2(8x-4)-2 x<14x+12
16x - 8 - 2x < 14x + 12
-8 < 12
which is a true statement, thus your inequation is true for all values of x
so always
To determine whether the inequality 2(8x-4)-2x < 14x+12 is always true, sometimes true, or never true, we need to simplify it and analyze the results.
First, let's simplify the inequality:
Start with the left side:
2(8x-4)-2x
= 16x - 8 - 2x
= 14x - 8
Now, the inequality becomes: 14x - 8 < 14x + 12
Notice that both sides have 14x terms. By subtracting 14x from both sides, we can eliminate them:
-8 < 12
This inequality is true. Therefore, the statement "2(8x-4)-2x < 14x+12" is always true.
To determine whether the inequality 2(8x - 4) - 2x < 14x + 12 is always true, sometimes true, or never true, we need to simplify and solve the inequality.
Let's begin by simplifying the left side of the inequality:
2(8x - 4) - 2x = 16x - 8 - 2x = 14x - 8
Now we can rewrite the inequality as:
14x - 8 < 14x + 12
To solve the inequality, we want to isolate the variable x on one side. Let's do that:
14x - 14x < 12 + 8
0 < 20
Since 0 is always less than 20, the inequality 2(8x - 4) - 2x < 14x + 12 is true for all values of x. Therefore, the inequality is always true.
In summary, the inequality 2(8x - 4) - 2x < 14x + 12 is always true.