Given
Given
Transitive
substitution property of equality
Subtraction property of equality
Addition property of equality
multiplication property of equality
Simplify
simplify
What is substitution?
Substitution means putting numbers in place of letters to calculate the value of an expression.
What is transitive property?
The transitive property states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”
What is addition and subtraction property of equality?
The addition and subtraction property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.
What is multiplication property of equality?
The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.
According to the given question.
AB = BC and BC = CD ( Given)
AB = 3x - 1 and CD = 2x + 3 ( Given)
Since,
AB = BC and BC = CD
⇒ AB = CD (transitive)
Substitute the value of AB and CD in AB = CD
⇒ [tex]3x - 1 = 2x + 3[/tex] (substitution property of equality)
⇒ [tex]x -1= 3[/tex] (subtraction property of equality)
⇒ [tex]x = 4[/tex] (Addition property of equality)
Since,
AB = BC
⇒ AB= 3x -1
⇒ [tex]AB = 3(4) - 1[/tex] ( multiplication property of equality)
⇒ [tex]AB = 11[/tex] (simplify)
Therefore,
BC = 11 (simplify)
Find out more information about substitution, addition, subtraction and transitive property of equality here:
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