Respuesta :
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,
[tex]\rightarrow \frac{1}{3} \text{ of number } = \frac{1}{3} \times x = \frac{x}{3}[/tex]
Thus from given statement,
one-third of a number x is greater than five less than twice the number
[tex]\text{ one-third of a number x } > \text{ five less than twice the number x }[/tex]
[tex]\frac{x}{3} > 2x - 5[/tex]
Solve the above inequality
Multiply both sides of inequality by 3
[tex]\frac{x}{3} \times 3 > (2x - 5) \times 3[/tex]
[tex]x > 3(2x-5)[/tex]
Solve for brackets in R.H.S
[tex]x > 6x - 15[/tex]
Add -6x on both sides of inequality
[tex]x - 6x > 6x - 15 -6x\\\\-5x>-15[/tex]
Multiply both sides of inequality by -1
Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign
[tex]5x < 15[/tex]
Divide both sides of inequality by 5
[tex]x < 3[/tex]
Thus the true inequality is x < 3
