8x + 16 = 2(4x + 8) = 4(2x + 4) = 8(x + 2) = 16((1/2)x + 1) = -8(-x - 2)
Equivalent expressions
To determine if the expressions (xx + 3) and (xx + 6 + xx) are equivalent, we can simplify them. The second expression simplifies to (2xx + 6). Since (xx + 3) and (2xx + 6) are not the same, they are not equivalent expressions.
Expressions equivalent to (9x) include (3(3x)), (18 \cdot \frac{x}{2}), and (\frac{27x}{3}). Any expression that can be simplified to (9x) through multiplication or division by non-zero constants is also equivalent.
The expressions equivalent to (81x) include (9^2x) (since (81 = 9^2)), (3^4x) (since (81 = 3^4)), and (x \cdot 81). Additionally, (81 \cdot x) and (x \cdot 81) are also equivalent forms. All these expressions represent the same quantity.
No because -3-(-9) = 6 but -9-3 = -12
the answer is a(n) equationequationWhen two expressions are equivalent they can form an equation.
Equivalent expressions.
Equivalent ExpressionDefinition of Equivalent ExpressionTwo algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.More about Equivalent ExpressionTo symbolize equivalent expressions an equality (=) sign is used.Examples of Equivalent Expression3(x + 3) and 3x + 9 are equivalent expressions, because the value of both the expressions remains same for any value of x. For instance, for x = 4, 3(x + 3) = 3(4 + 3) = 21 and 3(x + 9) = 3 × 4 + 9( x + 3) = 21.The expressions 6(x2 + y + 2) and 6x2 + 6y + 12 are equivalent expressions and can also be written as 6(x2 + y + 2) = 6x2 + 6y + 12.Solved Example on Equivalent ExpressionChoose an expression that is equivalent to the expression 2n + 7(3 + n).Choices:A. 9n + 21B. -9n + 21C. -9n - 21D. n + 21Correct Answer: ASolution:Step 1: 2n + 7(3 + n) [Original expression.]Step 2: = 2n + 7(3) + 7(n) [Use the distributive property.]Step 3: = 2n + 21 + 7n [Multiply.]Step 4: = 2n + 7n + 21 [Use the commutative property.]Step 5: = 9n + 21 [Combine like terms.]well....in a totally inataquitly way...theotorical...e=mc2
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Two algebraic expressions that have the same value are called equivalent expressions. For example, (2(x + 3)) and (2x + 6) are equivalent because they simplify to the same value for any value of (x). This equivalence can be verified by substituting values for (x) or by simplifying the expressions.
equivalent expressions
Equivalent ExpressionDefinition of Equivalent ExpressionTwo algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.More about Equivalent ExpressionTo symbolize equivalent expressions an equality (=) sign is used.Examples of Equivalent Expression3(x + 3) and 3x + 9 are equivalent expressions, because the value of both the expressions remains same for any value of x. For instance, for x = 4, 3(x + 3) = 3(4 + 3) = 21 and 3(x + 9) = 3 × 4 + 9( x + 3) = 21.The expressions 6(x2 + y + 2) and 6x2 + 6y + 12 are equivalent expressions and can also be written as 6(x2 + y + 2) = 6x2 + 6y + 12.Solved Example on Equivalent ExpressionChoose an expression that is equivalent to the expression 2n + 7(3 + n).Choices:A. 9n + 21B. -9n + 21C. -9n - 21D. n + 21Correct Answer: ASolution:Step 1: 2n + 7(3 + n) [Original expression.]Step 2: = 2n + 7(3) + 7(n) [Use the distributive Definition_for_Equivalent_Expressions.]Step 3: = 2n + 21 + 7n [Multiply.]Step 4: = 2n + 7n + 21 [Use the commutative property.]Step 5: = 9n + 21 [Combine like terms.]