Simplifying Equations

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Math › Simplifying Equations

Questions 1 - 4

1

Solve the following equation for x in terms of the other variables:

$\frac{ax}{b-ax}=2$

$x=\frac{2b}{3a}$

$x=\frac{3b}{2a}$

$x=\frac{2a}{3b}$

$x=\frac{3a}{2b}$

Explanation

$\frac{ax}{b-ax}=2$

Multiply both sides by to get:

Distribute the :

Combine like terms:

Divide both sides by :

$x=\frac{2b}{3a}$

2

Simplify the fraction to the lowest terms:

$\frac{924}{1092}$

$\frac{11}{13}$

$\frac{44}{52}$

$\frac{308}{364}$

Cannot be simplified

Explanation

Find the common multiple between the numerator and denominator.

$\frac{924}{1092}$

divide numerator and denominator by 3:

$\frac{308}{364}$

divide numerator and denominator by 7:

$\frac{44}{52}$

divide numerator and denominator by 4:

$\frac{11}{13}$

Cannot be divided any more- lowest terms.

3

Solve the following equation for x in terms of the other variables:

$x=\frac{a}{bc}$

$x=\frac{b}{c}$

$x=\frac{ab}{c}$

$x=\frac{bc}{a}$

$x=\frac{c}{ab}$

Explanation

Divide both sides by :

$x=\frac{a}{bc}$

4

If given the equation , with a positive integer, the result must be an integer multiple of:

5

10

8

2

12

Explanation

The mathematical expression given in the question is . Adding together like terms, , this can be simplified to . The expression can be factored as . For every positive integer , must be a multiple of 5. If , then , which is not an integer multiple of 2, 8, 10, or 15. Therefore, the correct answer is 5.

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