1. Equation involving cross multiplication1

2. Recap - Reducing Equation to the linear form by Cross multiplication
Numerator RHS
Denominator LHS
Numerator LHS
Denominator LHS
Is an Equation. We need convert into linear form (in a line) before we solve
By Cross multiplication, we convert the equation to linear form.
Cross Multiplying
Denominator of LHS with Numerator of RHS
Cross Multiplying
Numerator of LHS with Denominator of RHS
Where 'x' is the variable
a,b,c,d, m,n are numerals
Open Brackets by Multiplying , Transpose and Solve
Let us do some examples.

3. Transpose Variable from RHS to LHS Transpose Constant from LHS to RHS
Example 1: Solve:
Solution: Given
9 c – 3 = 2*(3c)
9c – 3 = 6c
9c - 6c = 3
3c = 3
Step 1:
Cross Multiply to convert equation to linear form
Step 2:
Open brackets RHS
Step 3:
Transpose Variable from RHS to LHS
Transpose Constant from LHS to RHS
Step 4:
Divide both sides by 3
Ans: c = 1

4. Transpose Variable from RHS to LHS
Example 2: Solve:
Solution: Given:
4 c = 7*(2c + 6)
4c = 14 c + 42
4c – 14 c = 42
-10c = 42
Step 1:
Cross Multiply to convert equation to linear form
Step 2:
Open brackets RHS
Step 3:
Transpose Variable from RHS to LHS
Step 4:
Divide both sides by -10
Simplify
Ans:

5. Example 3: Solve: Solution: Given: 5 c = 4*(3 – 2c) 5 c = 12 – 8 c
Step 1:
Cross Multiply to convert equation to linear form
Step 2:
Open brackets RHS
Step 3:
Transpose Variable from RHS to LHS
Step 4:
Divide both sides by 13
Ans:

6. Example 4: Solve: Solution: Given: z * 9 = 4*(z - 8) 9 z = 4z - 32
Step 1:
Cross Multiply to convert equation to linear form
Step 2:
Open brackets RHS
Step 3:
Transpose Variable from RHS to LHS
Step 4:
Divide both sides by 5
Ans:

7. Solve: 1. 4x/(x + 6) = 5 2. 6x/(10 - 2x) = 2 3. z/(z- 5) = 4/9
Try these
Solve:
1. 4x/(x + 6) = 5
2. 6x/(10 - 2x) = 2
3. z/(z- 5) = 4/9