All ACT Math Resources
Example Question #453 : Algebra
Which of the following inequalities defines the solution set for the inequality 14 – 3x ≤ 5?
x ≥ 3
x ≤ –19/3
x ≤ –3
x ≥ –3
x ≤ 3
x ≥ 3
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.
Example Question #1944 : Act Math
Solve 6x – 13 > 41
x < 6
x > 6
x > 9
x > 4.5
x < 9
x > 9
Add 13 to both sides, giving you 6x > 54, divide both sides by 6, leaving x > 9.
Example Question #34 : Inequalities
Solve for .
When dividing both sides of an inequality by a negative number, you must change the direction of the inequality sign.
Example Question #455 : Algebra
Solve 3 < 5x + 7
2 > x
Subtract seven from both sides, then divide both sides by 5, giving you –4/5 < x.
Example Question #1945 : Act Math
Find is the solution set for x where:
We start by splitting this into two inequalities, and
We solve each one, giving us or .
Example Question #1 : How To Find The Solution To An Inequality With Division
Which of the following could be a value of , given the following inequality?
The inequality that is presented in the problem is:
Start by moving your variables to one side of the inequality and all other numbers to the other side:
Divide both sides of the equation by . Remember to flip the direction of the inequality's sign since you are dividing by a negative number!
The only answer choice with a value greater than is .
Example Question #205 : Algebra
Solve for the -intercept:
Don't forget to switch the inequality direction if you multiply or divide by a negative.
Now that we have the equation in slope-intercept form, we can see that the y-intercept is 6.
Example Question #3 : How To Find The Solution To An Inequality With Division
Solve for :
Begin by adding to both sides, this will get the variable isolated:
Next, divide both sides by :
Notice that when you divide by a negative number, you need to flip the inequality sign!
Example Question #181 : Equations / Inequalities
Each of the following is equivalent to
xy/z * (5(x + y)) EXCEPT:
5x²y + 5xy²/z
xy(5x + 5y)/z
5x² + y²/z
xy(5y + 5x)/z
5x² + y²/z
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.
Example Question #5 : Inequalities
What is the solution set of the inequality ?
We simplify this inequality similarly to how we would simplify an equation