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

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Whether the statement &quot;The equations 5x−4=2x and3x=4 are equivalent equations&quot; is true or false.

delilnaT · Accepted Answer

Formula used: Addition property for inequalities: For any real number a, b and c, a&amp;lt;b is equivalent to a+c&amp;lt;b+c and a&amp;gt;b is equivalent to a+c&amp;gt;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&amp;lt;b is equivalent to ac&amp;lt;bc and a&amp;gt;b is equivalent to ac&amp;gt;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 5x−4=2x. Simplify the equation 5x−4=2x as follows. 5x−4=2x 5x−4+4=2x+4 [Add 4 to both sides] 5x=2x+4 5x−2x=2x+4−2x [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 &quot;The equations 5x−4=2x and 3x=4 are equivalent equations&quot; is true.

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

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