Multi-Step Equations & Inequalities
Why So Literal Equations?
All Things Slope
What's the Equation?
Put an Exponent in It
Math Vocabulary Because I'm Also an ELA Teacher
100
Solve for x.
14x + 8 = 64
x = 4
100
Solve for width (w).
A=lw
A/l=w
100
What is the slope of this equation?
y=-7x+12
m=-7
100
The formula listed below can be used to find the area of a circle. Solve the equation for r.
A=πr^2
√A/π = r
100
Simplify.
x^4m^3 xx x^2m^8
x^6m^11
100
This three word phrase explains and measures the change in y (rise) over x (run). It's another name for the slope.
rate of change
200
Is 100 a possible solution to the following inequality?
1/5x + 18 > 30
Yes, because x > 60.
200
Solve for x.
g=-3x-2
x=(-g-2)/3
200
Determine the slope of a line that passes through the following points: (-10, 2) and (5, 7).
m=1/3
200
Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 26.4 mph and is decreasing his speed by 0.7 mph each second. Write an equation to represent when Mike and Hank will match speed.
12+0.2x=26.4-0.7x
200
Simplify.
(x^12y^5)/(x^10y
x^2y^4
200
What does the b stand for in the following slope equation?
y=mx+b
y-intercept
300
Solve for x.
5(x+3) = 6x - 3x - 9
x = -12
300
Solve for x.
k/x = w-v
x=k/(w-v)
300
Write an equation for the line that passes through the point (1, 7) with a slope of -2.
y-7=-2(x-1)
y=-2x+9
300
Angela is shopping for pet supplies and needs to buy a kennel and several toys. At Paws R Us she would pay $50.75 for the kennel and $3.75 for each pet toy. At Truth or Tail she would pay $43.25 for the kennel and $5 for each pet toy.
Write an inequality to represent x, the number of pet toys Angela would need to buy for Paws R Us to be the cheaper option.
50.75+3.75x<43.25+5x
300
Simplify. There should be only positive exponents.
(a^3b^4)/(a^6b^3) xxb^-2
1/(a^3b)
300
When there is an equals sign (=) present, you have an equation.
When there is an inequality sign (<,>) present, you have an inequality.
What is the word that describes multiple terms but no equal sign like in the following example?
2c+4
(algebraic) expression
400
Is 16 a possible solution to the inequality?
-4/5n+1/5(n+55)<44
Yes, because x > -55.
400
Solve for a.
gc=(a+b)/a
a=b/(gc-1)
400
Write the following equation in Standard Form.
4y=3x+14
3x-4y=-14
400
Mia bought a used car for $9,500. It is expected that the value of the car will decrease by an average of $750 each year. Write a linear equation that can be used to find y, the value of the car in x years after Mia purchased it?
y=9500-750x
400
Simplify. There should only be positive exponents in your answer.
(2x^2y)^4/(16x^3y^6)
x^5/y^2
400
The zero is another name for this point on a graph where Y is equal to 0.
x-intercept
500
Solve for n.
4(6n-9) = 6(4n-10)
No Solution
500
The volume formula for a special shape is listed below. Determine the formula to find a.
V=1/3A(a+b)
a=(3V)/A -b
500
Write the equation of the graphed inequality.
y≤8/5x+5
500
Mitch is a trainer. He charges customers $75/hour for personal sessions and $25/hour for group sessions. Last week Mitch earned no more than $650. Write an inequality that represents the possible combinations of x personal sessions and y group sessions that Mitch trained.
75x+25y≤650
500
Simplify. Your answer should contain only positive exponents.
((m^2)^3 xx -2m^3p^-3)/(m^3p^3)
(-2m^6)/p^6
500
When a base has an exponent of 1/3, that is the same thing as taking this.
z^(1/3)
cube root