How to find the solution to an inequality with subtraction - ACT Math
Card 0 of 6
Given that x = 2 and y = 4, how much less is the value of 2_x_2 – 2_y_ than the value of 2_y_2 – 2_x_ ?
Given that x = 2 and y = 4, how much less is the value of 2_x_2 – 2_y_ than the value of 2_y_2 – 2_x_ ?
First, we solve each expression by plugging in the given values for x and y:
2(22) – 2(4) = 8 – 8 = 0
2(42) – 2(2) = 32 – 4 = 28
Then we find the difference between the first and second expressions’ values:
28 – 0 = 28
First, we solve each expression by plugging in the given values for x and y:
2(22) – 2(4) = 8 – 8 = 0
2(42) – 2(2) = 32 – 4 = 28
Then we find the difference between the first and second expressions’ values:
28 – 0 = 28
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The cost, in cents, of manufacturing 
pencils is 
, 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?
The cost, in cents, of manufacturing
If each pencil sells at 50 cents, 
pencils will sell at 
. The smallest value of 
such that
If each pencil sells at 50 cents,
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Solve 
Solve
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 
.
Absolute value problems are broken into two inequalities:
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Which of the following inequalities defines the solution set to 
?
Which of the following inequalities defines the solution set to
First, move the 
s to one side.
Subtract by 1
Divide both sides by 7.
First, move the
Subtract by 1
Divide both sides by 7.
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Solve the following inequality:
Solve the following inequality:
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.
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.
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Solve the following inequality:
Solve the following inequality:
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,
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,
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