Is the following inequality always,sometimes,never,true 2(8 x-4)-<14 x+12
2(8 x-4)-<14 x+12
16 x - 8 ≤ 14x + 12
2x ≤ 20
x ≤ 10
what do you think?
To determine whether the inequality 2(8x - 4) ≤ 14x + 12 is always true, sometimes true, or never true, we need to compare the left side (2(8x - 4)) with the right side (14x + 12). Let's simplify the inequality step by step.
First, distribute the 2 on the left side:
2(8x - 4) ≤ 14x + 12
16x - 8 ≤ 14x + 12
Next, let's isolate the x term on one side and the constant terms on the other side:
16x - 14x ≤ 12 + 8
2x ≤ 20
Now, divide both sides of the inequality by 2 to solve for x:
(2x)/2 ≤ 20/2
x ≤ 10
Therefore, the simplified inequality is x ≤ 10.
To determine if the inequality 2(8x - 4) ≤ 14x + 12 is always true, sometimes true, or never true, we consider all possible values of x. In this case, any value of x less than or equal to 10 will satisfy the inequality. Thus, the inequality is true for values of x less than or equal to 10, making the statement "2(8x - 4) ≤ 14x + 12" sometimes true.