Search results
People also ask
Are two algebraic expressions equivalent?
What is an example of an equivalent expression?
How do you identify an equivalent expression?
How do students generate equivalent expressions?
Equivalent expressions examples ↓ Example 1: addition and subtraction Example 2: addition and subtraction Example 3: distributive property Example 4: addition and subtraction Example 5: combining like terms Example 6: two step with distributive property
- Overview
- What are equivalent expressions?
- What skills are tested?
- How do we recognize equivalent expressions?
- How do we solve for unknown coefficients?
- How do we rearrange formulas?
- Your turn!
- Things to remember
What are equivalent expressions?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
[Examples]
•Distributing coefficients and combining like terms in algebraic expressions
•Recognizing equivalent algebraic expressions
•Solving for an unknown coefficient using two equivalent expressions
•Rearranging formulas containing 2 or more variables
Questions about equivalent expressions usually feature both
and
. To check which complex expression is equivalent to the simple expression:
1.Distribute any coefficients: a(bx±c)=abx±ac .
2.Combine any like terms on each side of the equation: x -terms with x -terms and constants with constants.
3.Arrange the terms in the same order, usually x -term before constants.
Some questions will present us with an equation with algebraic expressions on both sides. On one side, there will be an unknown coeffient, and the question will ask us to find its value.
For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if ax+b=cx+d for all values of x , then:
•a must equal c .
•b must equal d .
To find the value of unknown coefficients:
1.Distribute any coefficients on each side of the equation.
Formulas are equations that contain 2 or more variables; they describe relationships and help us solve problems in geometry, physics, etc.
Since a formula contains multiple variables, sometimes we're interested in writing a specific variable in terms of the others. For example, the formula for the area, A , for a rectangle with length l and width w is A=lw . It's easy to calculate A using the formula if we know l and w . However, if we know A and w and want to calculate l , the formula that best helps us with that is an equation in which l is in terms of A and w , or l=Aw .
Just as we can add, subtract, multiply, and divide constants, we can do so with variables. To isolate a specific variable, perform the same operations on both sides of the equation until the variable is isolated. The new equation is equivalent to the original equation.
[Example]
TRY: IDENTIFYING EQUIVALENT EXPRESSIONS
Which of the following expressions is equivalent to 4x−3 for all values of x ?
Choose 1 answer:
Choose 1 answer:
•(Choice A)
2(2x−3)
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To check whether a more complex expression is equivalent to a simpler expression:
1.Distribute any coefficients: a(bx±c)=abx±ac
2.Combine any like terms on each side of the equation: x -terms with x -terms and constants with constants
3.Arrange the terms in the same order, usually x -term before constants.
4.If all of the terms in the two expressions are identical, then the two expressions are equivalent.
Nov 21, 2023 · An equivalent expression is an expression that has the same value or worth as another expression, but does not look the same. An algebraic example of equivalent...
- How can you write equivalent expressions?Equivalent expressions can be written using numbers, grouping symbols, and mathematical operations. They can be written using variables, constants...
- What is an example of an equivalent expression?An example of an equivalent expression is to think about money. There is more than one representation of twenty-five cents. A quarter, 2 dimes an...
- How do you identify equivalent expressions?Equivalent expressions can be identified by using the distributive property, combining like terms, factoring, or by substituting the same value for...
Let’s look at some more examples of equivalent expressions. What are equivalent expressions? Addition is commutative which means the order in which we add the terms is not important – the answer will be the same. For example, 3x+7y\equiv7y+3x. 3x + 7y ≡ 7y + 3x. 3x+7y 3x + 7y is the same as 7y+3x 7y + 3x because the values of the variables match.
Examples, videos, and solutions to help Grade 7 students learn how to generate equivalent expressions by using commutative property and associative property.
Dec 18, 2023 · 3 × 2 x − 3 × 1 + 2 × x + 2 × 1. = 6x – 3 +2x + 2. Combining the like terms, we get. (6x + 2x) + (-3 + 2) = 8x – 1. 8x – 1 is an equivalent expression to 3 (2x – 1) + 2 (x + 1). How to find equivalent algebraic expressions described with the two ways to write them with examples.
Examples, solutions, videos, and lessons to help Grade 6 students learn to apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the ...
