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

Solve the following inequality:

Explanation

To solve an inequality with subtraction, simply solve it is as an equation.

The goal is to isolate the variable on one side with all other constants on the other side. Perform the opposite operation to manipulate the inequality.

In this case add two to each side.

Solve

Explanation

Absolute value problems are broken into two inequalities: and . Each inequality is solved separately to get and . Graphing each inequality shows that the correct answer is .

Solve the following inequality:

$x<\frac{5}{3}$

$x>\frac{5}{3}$

Explanation

To solve, simply treat it as an equation.

This means you want to isolate the variable on one side and move all other constants to the other side through opposite operation manipulation.

Remember, you only flip the inequality sign if you multiply or divide by a negative number.

Thus,

$3x-7<5\Rightarrow 3x<12\Rightarrow x<4$

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