To solve this inequality, you should first subtract 14 from both sides.

This leaves you with –3x ≤ –9.

In the next step, you divide both sides by –3, remembering to flip the inequality sign when you do this.

This leaves you with the solution x ≥ 3.

If you selected x ≤ 3, you probably forgot to flip the sign. If you selected one of the other solutions, you may have subtracted incorrectly.

Add 13 to both sides, giving you 6x > 54, divide both sides by 6, leaving x > 9.

\(\displaystyle \small 14-2x\geq22\)

\(\displaystyle \small -2x\geq8\)

When dividing both sides of an inequality by a negative number, you must change the direction of the inequality sign.

\(\displaystyle \small x\leq-4\)

Subtract seven from both sides, then divide both sides by 5, giving you –4/5 < x.

We start by splitting this into two inequalities, \(\displaystyle (5x-3)>12\) and \(\displaystyle (5x-3)< -12\) 

We solve each one, giving us \(\displaystyle x>3\) or \(\displaystyle x< \frac{-9}{5}\right\).

The inequality that is presented in the problem is:

\(\displaystyle 8-7x\leq11x+4\)

Start by moving your variables to one side of the inequality and all other numbers to the other side:

\(\displaystyle -7x-11x\leq4-8\)

\(\displaystyle -18x\leq-4\)

Divide both sides of the equation by \(\displaystyle -18\). Remember to flip the direction of the inequality's sign since you are dividing by a negative number!

\(\displaystyle x\geq\frac{-4}{-18}\)

Reduce:

\(\displaystyle x\geq\frac{2}{9}\)

The only answer choice with a value greater than \(\displaystyle \frac{2}{9}\) is \(\displaystyle \frac{4}{9}\).

Don't forget to switch the inequality direction if you multiply or divide by a negative.

\(\displaystyle 3y+11\geq 5y+6x-1\)

\(\displaystyle -2y+11\geq6x-1\)

\(\displaystyle -2y\geq6x-12\)

\(\displaystyle -\frac{1}{2}(-2y\geq 6x-12)\)

\(\displaystyle y\leq -3x+6\)

Now that we have the equation in slope-intercept form, we can see that the y-intercept is 6.

Begin by adding \(\displaystyle 12\) to both sides, this will get the variable isolated:

\(\displaystyle -4x < 15 + 12\)

Or...

\(\displaystyle -4x < 27\)

Next, divide both sides by \(\displaystyle -4\):

\(\displaystyle x > -\frac{27}{4}\)

Notice that when you divide by a negative number, you need to flip the inequality sign!

Choice a is equivalent because we can say that technically we are multiplying two fractions together: (xy)/z and (5(x + y))/1.  We multiply the numerators together and the denominators together and end up with xy (5x + 5y)/z.  xy (5y + 5x)/z is also equivalent because it is only simplifying what is inside the parentheses and switching the order- the commutative property tells us this is still the same expression.  5x²y + 5xy²/z is equivalent as it is just a simplified version when the numerators are multiplied out.  Choice 5x² + y²/z is not equivalent because it does not account for all the variables that were in the given expression and it does not use FOIL correctly.

We simplify this inequality similarly to how we would simplify an equation

\(\displaystyle \dpi{100} \small 3x+8-8< 35-8\)

\(\displaystyle \dpi{100} \small \frac{3x}{3}< \frac{27}{3}\)

Thus \(\displaystyle \dpi{100} \small x< 9\)