Integers & Order of Operations & Fractions
−7x(8)=?
explain how to solve
-56
- x + = -
Difference between ''less than'' and ''less than or equal to''.
(Less than): Smaller than a number, not including it. Example: x<5.
(Less than or equal to): Smaller than or exactly equal to a number. Example: x≤5.
Formula for y-intercept.
y=mx+b
2x−3y=7
y =3x−7
Solve using substitution.
(2, −1)
Adam is 20 years younger than Brian. In two years Brian will be twice as old as Adam. How old are they now?
B=2A
(x+2)=2(x−18)
x=38
Adam is 18 and Brian is 38.
7+(−10) x 2=?
Explain how to solve.
First step is multiplying. -10x2=-20
Second step is adding. Different signs, subtract 7+(-20)=7-20=-13, use sign from bigger number. Solution is -13.
4−2x=10
x=−3
Formula for slope.
Formula: desk
4x−2y=2
2x+y=−5
Solve using substitution.
(−1,−3)
Two joggers start from opposite ends of an 8 mile course running towards each other. One jogger is running at a rate of 4mph, and the other is running at a rate of 6 mph. After how long will the joggers meet?
4t+6t=8
t=4/5
48 minutes
5/6+4/9=?
explain the solution
23/18
3(2x−4)+9=15
x=3
Slope= 3/4 , y −intercept=−3
Slope−intercept equation?
y =3/4x−3
Explain steps of solving systems of equation using graph.
1. Simplify systems of equation making similar to formula y=mx+b.
2. Find slope (m) and y-intercept (y).
3. Put to graph.
4. Find intercept point of lines.
Louis is 26 years old. Her daughter is 4 years old. In how many years will Louis be double her daughter’s age?
L=2D
(26+t)=2(4+t)
t=18
In 18 years she will be double her daughter′s age.
2+3(9−4)2
77
2−4|2x+3|=−18
x=1 and x=−4.
Find the slope between (−4,3) and (2,−9)
m=−2
Explain steps of solving systems of equation using substitution.
1. Find the lone variable.
2. Solve for the lone variable.
3. Substitute into the untouched equation.
4. Solve.
5. Plug into lone variable equation and evaluate.
Bob and Fred start from the same point and walk in opposite directions. Bob walks 2 miles per hour faster than Fred. After 3 hours they are 30 miles apart. How fast did each walk?
We know nothing about Fred, so use 'r' for his rate Bob is 'r+2', showing 2mph faster.
3r +6+3r=30
r = 4.
Bob traveled 6 miles per hour and Fred traveled 4 mph.
Integers include...
Integers include negative whole numbers, zero, and positive whole numbers.
3(2x−4)+4x<4(3x−7)+8
Solve and give interval notation.
x>4
(4, ∞)
y =2x+3
y =−x−3
Solve this system of equation using graphing.
( −2,−1)
x+y=5
x−y=−1
Solve using substitution method.
(2, 3)
Show me tables for age problem solving and distance problem solving separately.
Table