Algebra

Question 1

9y -18 = -4y + 4.

Find y.

Answer 1

9y -18 = -4y +4
= 9y + 4y = 18 + 4
=13y = 22
=13y/13 = 22/13
y=1.7

Question 2

14b + 26 = 7b - 6.

Find b.

Answer 2

14b + 26 = 7b - 6
= 14b -7b = -26 -6
=7b = -32
=7b/7 = -32/7
b=-4.6

Question 3

-26x - 15 = -5x + 10.

FInd x.

Answer 3

-26x - 15 = -5x + 10
=-26x + 5x = 15 + 10
=-21x = 25
=-21x/-21 = 25/-21
x=-1.2

Question 4

How do you add/subtract fractions?

Answer 4

1. Convert the denominator to the LCM, then add/subtract the numerators.

Question 5

Solve 3/6 + 7/12.

Answer 5

3/12 + 7/12
=10/12
=5/6

Question 6

Solve 37/44 - 30/88.

Answer 6

37/88 - 30/88

=7/88

Question 7

Solve 3/7 + 2/4

Answer 7

3/28 + 2/28

=5/28

Question 8

How do you multiply/divide algebraic fractions? List the two steps.

Answer 8

1. Cancel any common factors

2. Multiply the numerators and denominators.

Question 9

Factorise ab + ac

Answer 9

ab + ac = a(b + c)

Question 10

Factorise 4a - a^2

Answer 10

4a - a^2 = a(4 - a)

Question 11

Factorise 8b +4ab

Answer 11

8b + 4ab = 4b(2 + 1a)

Question 12

What is the highest common factor (HCF).

Answer 12

The highest common factor of two or more terms is the largest term that is a factor of all the other terms.

Question 13

How do you find the HCF (highest common factor)?

Answer 13

1. Find the HCF of the numbers.
2. Find the HCF of the variables.
3. Multiply them together.

Question 14

Expand and simplify (x+5)(x-1)

Answer 14

= x^2 - 1x + 5x - 5

= x^2 + 4x - 5

Question 15

Expand and simplify (b-4)(b+6)

Answer 15

= b^2 + 6b - 4b - 24

= b^2 + 2b -24

Question 16

Expand and simplify (a-7)(a+2)

Answer 16

= a^2 + 2a -7a -14

= a^2 -5a -14