Question

If one-third of a number, x, is greater than five less than twice the number, which of the following is true?​

Answer 1

Question:

If one-third of a number, x, is greater than five less than twice the number, which of the following is true?​ x < 3, x > -3, x > -3/5, x < 3/5

Answer:

Option A

The true inequality is x < 3

Solution:

Let the number be "x"

One third of number means that,

`\rightarrow (1)/(3) \text{ of number } = (1)/(3) * x = (x)/(3)`

Thus from given statement,

one-third of a number x is greater than five less than twice the number

`\text{ one-third of a number x } > \text{ five less than twice the number x }`

`(x)/(3) > 2x - 5`

Solve the above inequality

Multiply both sides of inequality by 3

`(x)/(3) * 3 > (2x - 5) * 3`

`x > 3(2x-5)`

Solve for brackets in R.H.S

`x > 6x - 15`

Add -6x on both sides of inequality

`x - 6x > 6x - 15 -6x\\\\-5x>-15`

Multiply both sides of inequality by -1

Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign

`5x < 15`

Divide both sides of inequality by 5

`x < 3`

Thus the true inequality is x < 3