Whether the statement "The equations 5x-4=2x\ and 3x=4 are equivalent equa

Alyce Wilkinson

Alyce Wilkinson

Answered question

2021-10-14

Whether the statement "The equations 5x4=2x and3x=4 are equivalent equations" is true or false.

Answer & Explanation

delilnaT

delilnaT

Skilled2021-10-15Added 94 answers

Formula used:
Addition property for inequalities:
For any real number a, b and c, a<b is equivalent to a+c<b+c and a>b is equivalent to a+c>b+c.
Similar statement hold for  and .
Multiplication property for inequalities:
For any real number a, and b and for any positive number c, a<b is equivalent to ac<bc and a>b is equivalent to ac>bc.
Similar statement hold for  and .
Distributive law:
For any real numbers a, b and c, a(b+c)=ab+ac.
Calculation:
Consider the equation 5x4=2x.
Simplify the equation 5x4=2x as follows.
5x4=2x
5x4+4=2x+4 [Add 4 to both sides]
5x=2x+4
5x2x=2x+42x [Add -2x to both sides]
On further simplification,
3x=4
(13)3x=4(13) [Multiply by (13) on both sides]
x=43
Now, consider the equation 3x=4.
Solve the above equation as follows.
3x=4
(13)3x=4(13) [Multiply by (13) on both sides]
x=43
The solution of both the equation is same and it is equivalent equation.
Thus, the statement "The equations 5x4=2x and 3x=4 are equivalent equations" is true.

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