Here are some examples:
- 1+1=2
- 2−0=2
- 7X=2X+5X
- 4X×(2+3)=8X+12X
- 8X+12X=20X
Practicing Equivalent Expressions
Exercise 1
Write an equivalent expression for the following:
0
Solution
We look for an expression that represents 0, for example:
0=5−5
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Exercise 2
3+3+3
Solution
To do this exercise, we must first work out that the expression represents 9 before looking for an equivalent form.
3+3+3=10−1
Exercise 3
7X
Solution
We look for a way to represent 7X, e.g.:
7x=4x+2x+x
Do you know what the answer is?
Exercise 4
13X−3
Solution
We look for an equivalent way of representing 13X and −3, for instance:
13x−3=15x−2x−2−1
Exercise 5
1.5X+8+6.5X
Solution
As the expression represents 8X+8, we need to look for an alternative way to represent each term:
1.5x+8+6.5x=10x−2x+5+3
Which of the following expressions are are equivalent?
Exercise 6
18X
2+9X
Solution
The expressions are not equivalent. One represents 18X while the other one represents 9X.
Exercise 7
20X
2×10X
Solution
The expressions are equivalent as both represent 20X.
Do you think you will be able to solve it?
Exercise 8
3+3+3+3
3×4
Solution
The expressions are equivalent because both represent the number 12.
Exercise 9
15X−30
45−15−5X+15X
Solution
The expressions are not equivalent. The first one represents 15X while the second one represents only 10X.
Exercise 10
0.5X×1
0.5X+0
Solution
The expressions are equivalent.
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Questions and Answers: Equivalent Expressions
What is an algebraic expression?
An algebraic expression is a combination of numbers, letters (representing unknown numbers), and arithmetic operations.
What are equivalent algebraic expressions?
They are algebraic expressions that have different structures but represent the same value.
How to find equivalent expressions?
We try to modify the structure of the expression so that the value it represents is not altered.
Do you know what the answer is?
Additional Examples
It is important that we learn to write equivalent algebraic expressions in their simplest form since this will be very useful when solving equations.
Exercise 1
Simplify 2x+5x+x
Solution:
To find an equivalent expression we add the coefficients of each term together.
(2+5+1)x=8x
Exercise 2
Reduce the expression 8m+8−6m+3
Solution:
We separate the terms that have m from those that do not and perform the indicated operations.
8m+8−6m+3=8m−6m+8+3=(8−6)m+11=2m+11
Exercise 3
Find a simpler equivalent form for the expression 8x+2y−3z+3y−4x+3z
Solution:
We first group the terms that have the same letter and then perform the indicated operations.
8x+2y−3z+3y−4x+3z=8x−4x+2y+3y−3z+3z=(8−4)x+(2+3)y+(−3+3)z=4x+5y+0z=4x+5y
Do you think you will be able to solve it?
Exercise 4
Simplify the expression 6x+1−2x+3. Then substitute the value x=3 in to both expressions and verify that you get the same numerical value.
Solution:
First we simplify the expression.
6x+1−2x+3=6x−2x+1+3=4x+4
Now we substitute x=3 in to both expressions.
6(3)+1−2(3)+3=18+1−6+3=18+1+3−6=22−6=16
4(3)+4=12+4=16
We do indeed get the same numerical value from both expressions.
Exercise 5
Solve the equation 5x+2+3x+7−2x−5=16
Solution:
First, find an equivalent expression:
5x+2+3x+7−2x−5=16
5x+3x−2x+2+7−5=16
(5+3−2)x+4=16
6x+4=16
Now solve for x:
6x=16−4
6x=12
x=612
x=2
Examples with solutions for Equivalent Expressions
Exercise #1
18x−7+4x−9−8x=?
Video Solution
Step-by-Step Solution
To solve the exercise, we will reorder the numbers using the substitution property.
18x−8x+4x−7−9=
To continue, let's remember an important rule:
1. It is impossible to add or subtract numbers with variables.
That is, we cannot subtract 7 from 8X, for example...
We solve according to the order of arithmetic operations, from left to right:
18x−8x=10x10x+4x=14x−7−9=−16Remember, these two numbers cannot be added or subtracted, so the result is:
14x−16
Answer
Exercise #2
7.3⋅4a+2.3+8a=?
Video Solution
Step-by-Step Solution
It is important to remember that when we have numbers and variables, it is impossible to add or subtract them from each other.
We group the elements:
7.3×4a+2.3+8a=
29.2a + 2.3 + 8a =
37.2a+2.3
And in this exercise, this is the solution!
You can continue looking for the value of a.
But in this case, there is no need.
Answer
37.2a+2.3
Exercise #3
3m29m×63m=
Video Solution
Step-by-Step Solution
According to the laws of multiplication, we must first simplify everything into one exercise:
3m2×69m×3m=
We will simplify and get:
m2×69m2=
We will simplify and get:
69=
We will factor the expression into a multiplication:
3×23×3=
We will simplify and get:
23=1.5
Answer
Exercise #4
Are the expressions the same or not?
18x
2+9x
Video Solution
Answer
Exercise #5
Are the expressions the same or not?
20x
2×10x
Video Solution
Answer