Linear equations
Expanding brackets and factorization
Absolute Value/Formulae
Exponential Expressions
Solving Inequalities
100
Solve the equation 4x+3=23
4x+3=23 -3=-3 4x=20 /4=/4 x=5
100
5x(x-3)
***5x^2-15x*** 5x(x-3) 5x^2 -15x 5x^2-15x
100
If a=-1.7 then |a|=?
1.7
100
3*3=3² which equals?
9
100
5x-6<4
5x-6<4 +6 +6 5x<10 x>2 1. add 6 to both sides 2.divide each side by 5 3. change the sign
200
solve the equation 8(x-6)=32
8(x-6)=32 /8=/8 x-6=4 +6=+6 x=10
200
3xy+9xy^2+6x^2y
***3xy(1+3y+2x)*** 3xy(1)+3xy(3y)+3xy(2x) 3xy(1+3y+2x)
200
a=6 b=7 |a-b|=?
|a-b|=|6-7|=|-1|=1
200
2*2*2=2³ which equals?
8
200
18-4x≥2
18-4x≥2 -18 -18 -4x≥16 x≤-4 1. subtract 18 2. divide by -4 3. change sign
300
solve the equation 9-2x=3
9-2x=3 -9=-9 -2x=-6 /-2=/-2 x=3
300
x(x^2y-y^2+x)
***x^3y-xy^2+x^2*** x(x^2y) x(-y^2) x(x) x^3y-xy^2+x^2
300
v=u-gt to get t
***v-u/-g=t*** v=u-gt -u -u v-u=-gt v-u/-g=t
300
-2*-2*-2*-2= (-2)⁴ which equals?
16
300
24+6x>9+3x
24+6x>9+3x -3x -3x 24+3x>9 3x>-15 x<-5 1. subtract 3x 2. subtract 24 3. divide by 3 4. change sign
400
Solve the equation 3(2+3x)=5(4-x)
3(2+3x)=5(4-x) 6+9x=20-5x +5x=+5x 6+14x=20 -6=-6 14x=14 /14=/14 x=1
400
x^2+2xy+5x^3+10x^2y
***x(1+5x)(x+2y)*** x(x+2y)+5x^2(x=2y) (x+5x^2)(x+2y) x(1+5x)(x+2y)
400
c=2πr to get r
***c/2π=r*** c=2πr divide 2π c/2π=r
400
Formula: a^-n=1/a^n 4^-2=?
4^-2=1/4²=1/16=.0625
400
2(x-4)<16
2(x-4)<16 2x-8<16 +8 +8 2x<24 x>12 1. Distribute 2. add 8 3. divide by 2 4. change sign
500
Solve the equations 3x+4y=17 and 2x+5y=16
Answer: Graphical method. Geometrically you could consider these two linear equations are two straight lines. Find the intersection between these two lines by graphing and the point will give the values for x and y. Substitution method. 3x+4y=17 2x+5y=16 2x+5y=16 Rearrange one of the equations -2x =-2x to make y the subject 5y=16-2x /5=/5 y=(16/5 - 2/5x) 3x+4(16/5 -2/5x)=17 Substitute for y in the other 3x+64/5 - 8/5x=17 equation 5*(3x+64/5 - 8/5x=17) 15x +64-8x=85 Solve equation for x -64=-64 15x-8x=21 7x=21 x=3 3(3) +4y=17 9+4y=17 4y=8 y=2 Solution is x=3, y=2 Elimination method. 3x+4y=17 (1) 2x+5y=16 (2) Multiply the equation (1) by 2 and (2) by 3 6x+8y=34 (3) 6x+15y=48 (4) Subtract the equations. (4) -(3) 7y=14 y=2 3x+4(2)=17 3x+8=17 3x=9 x=3 the solution is x=3, y=2
500
2(3x+4)+4(x−1)
***10x+4*** 2(3x+4)+4(x−1) 2(3x)+2(4)+4(x)+4(-1) 6x+8+4x−4 combine like terms 10x+4
500
v=4/3πr^2 to get r
***√3V/4π=r*** v=4/3πr^2 v(3/4π)=4/3πr^2(3/4π) 3v/4π=r^2 square root on each side √3V/4π=r
500
Formula: a^-n=1/a^n 10^-3=?
10^-3=1/10³=1/1000=0.001
500
4(x-5)≥-1(x+10)
4(x-5)≥-1(x+10) 4x-20≥-x-10 5x-20≥-10 +20 +20 5x≥10 x≤2 1. distribute both sides 2. add x 3. add 20 4. divide by 5 5.change sign
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