SOLVING INEQ.
SOLVING INEQ.
LINEAR EQUATIONS
LINEAR SYSTEMS
MIXED
100
x + 2 − 2 > 12 − 2
x>10
combine like terms if you can so 2-2=0 and 12-2=10 so you get x>10
100
The direction x<7 is going on a number line.
What is going left?
100
3x+12=6
x=-2
subtract 12 on both sides and divide by 3 to find your answer
100
-X+2y=4
x+3y=1
What is the value of X?
X = -2
add both equations and get rid of one of the variables. In this problem -x and x cancel out so there is no extra steps. You should be left with 5y=5. Dividing both sides by 5 reveals that y=1 but we are looking for x. Plug in y to one of the equations and solve for X.
x+3(1)=1
x+3=1
x=-2
100
40x+60=180
Answer: x=30
Explanation:
Solve for x by subtracting 60 from both sides and then dividing 40.
200
12>2y+7
5>2y or 5/2>y
subtract 7 on both sides then divide by 2 to simplify further.
200
The sign ≥ means what in a number line?
closed circle looking to the right
200
3(5)-3x=12
x=1
multiply 3 and 5 then subtract what you got on both sides. Lastly divide by -3 to find your answer.
200
x-y=6
x+3y=2
What is the value of 3x+2?
Answer: 17
Explanation:
First you have to cancel out one of the variables. We can multiply the top equation by 3 to get 3x-3y=18 because 3y cancels out -3y. then add both equations and you should get 4x=20. Divide by 4 to get x=5. The question asks for 3x+2 so if we substitute you should get 3(5)+2=17
200
10x>2+3x
x>2/7
Subtract 3x on both sides and you should get 7x>2
Then divide by 7 on both sides to find your answer.
300
x+3<7
x<4
subtract 3 on both sides and you should get the inequality above.
300
The sign ≤ means what in a number line?
closed circle looking to the left
300
3(y+5)+5=20
y=0
Distribute the 3 into the parenthesis then add like terms. You should have 3y+20=20
subtract 20 on both sides and the divide by three on both sides which should give you your answer.
300
6x − 12y = 24
−x − 6y = 4
What is the value of xy?
Answer: -2
Explanation:
First you have to cancel out one of the variables. We can multiply the bottom equation by multiplying it by -2. You should get 2x+12y=-8. Add both equations, -12y and 12y cancel out leaving you with 8x=16. Divide by 8 and now you know x=2. To get Y you can substitute:
-(2)-6y=4
-6y=6
y=-1
xy= (2)(-1)
xy= -2
300
3x+9y=10
6x+2y=4
x=1/3 y=1
First multiply the top equation by 2 and you should get 6x+18y=20
Then subtract the top and bottom equation and you should get 16y=16 divide by 16 on both sides and you should get y=1 plug in y to find x.
400
-2y>-8+5
y<3/2
combine like terms so -8+5=-3
Then divide by -2 on both sides and switch the signs because you are dividing with a negative number.
400
Draw the graph of 3x ≤ 9.
You need to get X by itself so divide both sides by 3 and you should get x ≤ 3
400
2(10x+12)=10x+4
x=-2
Distribute the 2 into the parenthesis and you should get 20x+24=10x+4
Then subtract 10x and 24 on both sides. 10x=-20
Then divide by 10 on both sides which should give you your answer.
400
−8x − 10y = 24
6x + 5y = 2
What is the value of x?
Answer: x=7
First, cancel out one of the variables. We can cancel out Y by multiplying the bottom by 2 and getting 12x+10y=4. When you simplify, -10y and 10y cancel leaving you with 4x=28. Divide both sides by 4 to get x=7
400
6x + 8y = −22
y = −5
What is the value of X?
Answer: x=3
Explanation:
Substitute Y and solve for x:
6x+8(-5)=-22
6x-40=-22
6x=18
x=3
500
2y+3>-4
y>-7/2
First subtract by 3 on both signs so you should get 2y>-7 Divide by 2 on both sides and keep the sign the same because you are not dividing with a negative number.
500
Draw the graph of x+3 < 15x-11 on the white board.
First you need to get X by itself so you add 11 to both sides and subtract X from both sides. You should be left with 14<14x. If you rewrite it and divide both sides by 14 you should get x>1.
500
10x+25=35+5x
x=2
Subtract 5x on both sides and 25 on both sides. You should get 5x=10
Then divide by 5 on both sides and you should get your answer.
500
8x − 6y = −15
−16x + 7y = 30
What is the value of X?
500
What is the value of X?
Answer: x=-9
Explanation:
first combine 5/12 and -7/6 by making the denominators the same. -7/6 becomes -14/12. (5-14)/12 is -9/12. Multiply both sides by 12 and you end up with x=-9.