8(2y+18+3y) what is a equivalent expression
Right away we see that expressions (a), (b), and (d) are equivalent, since addition is commutative: $2x + 8 = 8 + 2x$. We now only have to check (c) and (e). If $x=0$, (c) and (e) have the value 4, whereas (a), (b), and (d) have the value 8.So (c) and (e) are not equivalent to (a), (b), and (d).Moreover, if $x=1$, then (c) has the value 6 and (e) has the value 5, so those two expressions are not equivalent either.For (c), we can use the distributive property and decompose one of the numbers to write two equivalent expressions: $$ \begin{align} &2x+4 \\ &2(x+2) \\ &2(x+1+1) \end{align} $$.o (c) and (e) are not equivalent to (a), (b), and (d). Moreover, if $x=1$, then (c) has the value 6 and (e) has the value 5, so those two expressions are not equivalent either. For (c), we can use the distributive property and decompose one of the numbers to write two equivalent expressions: Example 1: Write an equivalent expression for 2(x - 4) + 3. Answer: 2x - 8 + 3 = 2x - 5 Example 2: In the following equation, a and b are both integers. a(2x... - 3) = b - 10x Solve for the values of a and b by comparing equivalent expressions.y (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. 2^3 x 2^5 = 2^(3+5) = 2^8 = 256). 1 Example 1: Write an equivalent expression for 2(x - 4) + 3. 2  Answer: 2x - 8 + 3 = 2x - 5 Example 2: In the following equation, a is an integer. 3  a(x - 3) = 4x - 12. 4  Solve for the value of a by comparing equivalent expressions.5  Answer: ax - 3a = 4x - 12 gives a = 4. Check: 4(x - 3) = 4x - 12.y (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. 2^3 x 2^5 = 2^(3+5) = 2^8 = 256). ©Curriculum Associates, LLC Copying is not permitted.L14: Equivalent Linear Expressions 127Part 1: Introduction Lesson 14Find Out More Expressions that have the same value are called equivalent expressions. Numerical expressions such as 8 1 2, 15 2 5, 40 4 4, and 2 3 5 are all equivalent.Curriculum Associates, LLC Copying is not permitted.L14: Equivalent Linear Expressions 127Part 1: Introduction Lesson 14Find Out More Expressions that have the same value are called equivalent expressions. Numerical expressions such as 8 1 2, 15 2 5, 40 4 4, and 2 3 5 are all equivalent. Example of Equivalent Expressions. 3(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 x 4 + 9(x + 3) = 21.he expressions 6(x 2 + y + 2) and 6x 2 + 6y + 12 are equivalent expressions and can also be written as 6(x 2 + y + 2) = 6x 2 + 6y + 12. To symbolise equivalent expressions, people often simply use an equals sign. For example, they might say ‘ x + x + 4 = 2 x + 4’. The idea is that this is a statement that is always true, no matter what x is.However, it isn't really correct to write ‘1/ x + 1/ x = 2/ x ’ to indicate an equivalence of expressions, because this statement is not correct when x := 0.So instead, I will use the symbol ‘≡’, which you can read ‘is equivalent to’ (instead of ‘is equal to’ for ‘=’).owever, it isn't really correct to write ‘1/ x + 1/ x = 2/ x ’ to indicate an equivalence of expressions, because this statement is not correct when x := 0. So instead, I will use the symbol ‘≡’, which you can read ‘is equivalent to’ (instead of ‘is equal to’ for ‘=’). 166 L17: Equivalent Expressions Lesson 17 Part 1: Introduction Equivalent Expressions In Lesson 17 you learned to read, write, and evaluate expressions with variables. Now, take a look at this problem. Write an expression that is equivalent to (3  14)  27. Explore It Use the math you know to answer the question.hen continue exploring how to use properties of operations to write equivalent expressions with variables. Javier creates a rectangular painting. The painting is 3 feet long and more than 2 feet wide. The expression 3(2  x) represents the area of the painting.Write an expression equivalent to 3(2  x). Use the associative and commutative laws to write three expressions equivalent to: a) y +(3+x) b) (xy)3. The Distributive Laws The distributive laws are the basis of many procedures in both arithmetic and algebra.se the associative and commutative laws to write three expressions equivalent to: a) y +(3+x) b) (xy)3. The Distributive Laws The distributive laws are the basis of many procedures in both arithmetic and algebra. By (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. 2^3 x 2^5 = 2^(3+5) = 2^8 = 256).y (date), when given 5 mathematical expressions involving integer exponents, (name) will use the properties of integer exponents to generate an equivalent numerical expressions and the final integer value correctly for (4 out of 5) expressions (e.g. 2^3 x 2^5 = 2^(3+5) = 2^8 = 256). Therefore, the two expressions are equivalent. Example 3: Check whether the two expressions and equivalent. The first expression is the sum of 2 x 's and 3 y 's whereas the second one is the sum of 3 x 's and 2 y 's. Let us evaluate the expressions for some values of x and y.Take x = 0 and y = 1.So, there is at least one pair of values of the variables for which the two expressions are not the same.Therefore, the two expressions are not equivalent. Example 4: Check whether the two expressions and equivalent. Consider the first expression for any non-zero values of the variable.o, there is at least one pair of values of the variables for which the two expressions are not the same. Therefore, the two expressions are not equivalent. Example 4: Check whether the two expressions and equivalent. Consider the first expression for any non-zero values of the variable.
Expressions (a), (b), and (d) are equivalent