Solving Inequalities
x + 5 < 12
x < 7
The temperature must stay above freezing, which is 32*F. Write an inequality
T > 32
The sigh for the phrase "at most."
< (less than or equal to)
This type of line (solid or dashed) is used for a "greater than" or "less than" inequality when graphed.
A dashed or dotted line
The "rise over run" of a line
The slope
3p - 7 < (or equal to) 14
p < (or equal to) 7
You need to have at least 120 hours of community service. You have already completed 45 hours. Write an inequality to find the number of additional hours needed.
45 + h > (or equal to) 120
or h > (equal to) 75
The sigh for the phrase "no less than."
> (greater than or equal to)
Sarah is selling bracelets for $2 and earrings for $3. She wants to make at least 500. Write an inequality for her income with b for bracelets and $ for earrings.
2b + 3e > (or equal) 500
The slope of the line that passes through the points (2, 4) and (4, 5).
1/2
4 - 2y > (or equal to) 10
y < (or equal to) -3
A salesperson earns $50 per week plus $3 per sale. This week, they want their pay to be at least 100. Write an inequality for the number of sales
50 + 3y > (or equal) 100
This must be done to the inequality symbol when multiplying or dividing both sides by a negative number.
Flip or reverse the direction
Mandy buys soil for 5 per bag ($s) and plants for 12 each ($p). She can spend no more than $100. Write the inequality.
5s + 12p < (or equal) 100
The slope of any vertical line
Undefined
3x + 2 < 5x - 4
x > 3
The online course costs $25 per month plus $5 for each additional module. If a student's budget is 75, what is the maximum number of additional modules they can purchase?
m < (or equal) 10
The property that states: if a < (or equal) b and b < (or equal) c, then a < (or equal) c
The Transitive Property of Inequality
Katherine works no more than 20 hours total at two jobs (x and y). Write one inequality for the total hours worked.
x + y < (or equal) 20
The slope of any horizontal line
Zero
-2(m + 3) > 10
m < -8
A rectangular garden has 10 meters of fencing. If the length must be at least 2 meters, write an inequality for the possible width (w) of the garden.
w < (or equal) and w > 0
The property used when you add the same number to both sides of an inequality, keeping the sign the same.
The Addition Property of Inequality
For Katherine's job, she earns 8/hour baby sitting ($x) and 10/hour hosting ($y). She needs to earn at least 180. Along with x+y \le 20$, this is the second inequality for the system.
8x + 10y > (or equal) 180
-3