SAT Math - How to find the solution to an inequality with subtraction

Solve for :

Explanation

The correct method to solve this problem is to substract 5 from both sides. This gives .

Then divide both sides by negative 3. When dividing by a negative it is important to remember to change the inequality sign. In this case the sign goes from a less than to a greater than sign.

This gives the answer .

Solve for $x$ .

$-2x+5\leq 10$

$x\geq \frac{5}{2}$

$x\leq \frac{5}{2}$

$x\geq -\frac{5}{2}$

$x\leq 5$

$None\ of\ the\ above$

Explanation

Move +5 using subtraction rule which will give you $-2x\leq 5$ .

Divide both sides by 2 (using division rule) and you will get $-x\leq \frac{5}{2}$ which is the same as $x\geq \frac{5}{2}$

If 2 more than is a negative integer and if 5 more than is a positive integer, which of the following could be the value of ?

-7

Explanation

and , so and . The only integers between and are and .

If $\frac{a}{5}+5> 6$ , which of the following MUST be true?

I. $a> 2$

II. $a> 10$

III. $a< 6$

I only

II only

III only

I and II only

I, II, and III

Explanation

Subtract 5 from both sides of the inequality:

$\frac{a}{5}> 1$

Multiply both sides by 5:

$a> 5$

Therefore only I must be true.

Given $\left | 7x+9\right |>30$ , what is a possible value of ?

$-\frac{39}{7}$

Explanation

In order to find the range of possible values for $\left | 7x+9\right |>30$ , we must first consider that the absolute value applied to this inequality results in two separate equations, both of which we must solve:

and .

Starting with the first inequality:

Then, our second inequality tells us that

$x<-\frac{39}{7}(or -5\frac{4}{7})$

Therefore, is the correct answer, as it is the only value above for which (NOT greater than or equal to) or $x<-\frac{39}{7}$ (NOT less than or equal to).

Solve for .

$4x-8\geq 28$

$x\geq 9$

$x\leq 9$

Explanation

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

$4x-8\geq 28$ Add on both sides.

$4x\geq 36$ Divide on both sides.

$x\geq 9$

Solve for .

$x\leq -7$

$x\geq -7$

Explanation

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

Add on both sides.

Divide on both sides. Remember to flip the sign.

Solve for .

Explanation

We want to isolate the variable on one side and numbers on another side. Treat like a normal equation.

Add and subtract on both sides.

Divide on both sides.

The cost, in cents, of manufacturing $\dpi{100} \small x$ pencils is $\dpi{100} \small 1200+20x$ , where 1200 is the number of cents required to run the factory regardless of the number of pencils made, and 20 represents the per-unit cost, in cents, of making each pencil. The pencils sell for 50 cents each. What number of pencils would need to be sold so that the revenue received is at least equal to the manufacturing cost?

$\dpi{100} \small 40$

$\dpi{100} \small 33$

$\dpi{100} \small 36$

$\dpi{100} \small 27$

$\dpi{100} \small 30$

Explanation

If each pencil sells at 50 cents, $\dpi{100} \small x$ pencils will sell at $\dpi{100} \small 50x$ . The smallest value of $\dpi{100} \small x$ such that