Expressions, Equations, and Relationships>Determining Equivalence of Expressions with Models and Algebraic Representations(TEKS.Math.6.7.C)
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Texas 6th Grade Math › Expressions, Equations, and Relationships>Determining Equivalence of Expressions with Models and Algebraic Representations(TEKS.Math.6.7.C)
Expression A: $3x+12$; Expression B: $3(x+4)$. Are these expressions equivalent?
Yes. Apply the distributive property: $3(x+4)=3x+12$, which matches Expression A.
No. $3(x+4)$ equals $3x+4$, which is different from Expression A.
Yes. Both simplify to $x+16$.
No. Expression A has a variable but Expression B does not.
Explanation
They are equivalent. Using the distributive property, $3(x+4)=3x+12$, the same as Expression A.
Expression A: $5y+2y$; Expression B: $7y$. Are these expressions equivalent?
No. You cannot add terms with variables.
Yes. Combine like terms: $5y+2y=(5+2)y=7y$.
No. $5y+2y=5y^2$.
Yes. Since $5+2=10$, both equal $10y$.
Explanation
They are equivalent. $5y$ and $2y$ are like terms: $5y+2y=(5+2)y=7y$.
Expression A: $2(x+5)$; Expression B: $2x+5$. Which statement correctly determines if these expressions are equivalent?
Yes. Distributing gives $2x+5$.
Yes. Both simplify to $7x$.
No. $2(x+5)=2x+10$, not $2x+5$.
No. You cannot distribute a number to a variable.
Explanation
They are not equivalent. By the distributive property, $2(x+5)=2x+10$, which is different from $2x+5$.
Expression A: $-3(x-4)$; Expression B: $-3x+12$. Which shows why these expressions are equivalent?
Not equivalent because the signs are different.
Equivalent because $-3(x-4)=-3x-4$.
Not equivalent; a negative number cannot be distributed.
Equivalent. Distribute $-3$: $-3(x-4)=-3x+12$, which matches Expression B.
Explanation
They are equivalent. Distribute $-3$: $-3(x-4)=-3x+12$ because $-3\cdot(-4)=+12$.
Expression A: $3\left(x+\dfrac{1}{2}\right)$; Expression B: $3x+\dfrac{1}{2}$. Are these expressions equivalent?
No. Distribute: $3\left(x+\dfrac{1}{2}\right)=3x+\dfrac{3}{2}$, not $3x+\dfrac{1}{2}$.
Yes. The $3$ only multiplies $x$.
Yes. Both are equal to $3.5x$.
No. Fractions cannot be used with variables.
Explanation
They are not equivalent. By distribution, $3\left(x+\dfrac{1}{2}\right)=3x+\dfrac{3}{2}$, which is different from $3x+\dfrac{1}{2}$.