Algebra

Linear equations

100

Solve the equation 4x+3=23

4x+3=23 -3=-3 4x=20 /4=/4 x=5

200

solve the equation 8(x-6)=32

8(x-6)=32 /8=/8 x-6=4 +6=+6 x=10

300

solve the equation 9-2x=3

9-2x=3 -9=-9 -2x=-6 /-2=/-2 x=3

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

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

Expanding brackets and factorization

100

5x(x-3)

***5x^2-15x*** 5x(x-3) 5x^2 -15x 5x^2-15x

200

3xy+9xy^2+6x^2y

***3xy(1+3y+2x)*** 3xy(1)+3xy(3y)+3xy(2x) 3xy(1+3y+2x)

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

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)

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

Absolute Value/Formulae

100

If a=-1.7 then |a|=?

1.7

200

a=6 b=7 |a-b|=?

|a-b|=|6-7|=|-1|=1

300

v=u-gt to get t

***v-u/-g=t*** v=u-gt -u -u v-u=-gt v-u/-g=t

400

c=2πr to get r

***c/2π=r*** c=2πr divide 2π c/2π=r

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

Exponential Expressions

100

3*3=3² which equals?

9

200

2*2*2=2³ which equals?

8

300

-2*-2*-2*-2= (-2)⁴ which equals?

16

400

Formula: a^-n=1/a^n 4^-2=?

4^-2=1/4²=1/16=.0625

500

Formula: a^-n=1/a^n 10^-3=?

10^-3=1/10³=1/1000=0.001

Solving Inequalities

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

18-4x≥2

18-4x≥2 -18 -18 -4x≥16 x≤-4 1. subtract 18 2. divide by -4 3. change sign

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

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

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