How do you identify like terms in the expression 7x - 5x + 6 + 3x?

Like terms are terms that share the same variable raised to the same power. In 7x - 5x + 6 + 3x, the terms 7x, -5x, and 3x are like terms because they all have the variable x to the power of 1. Their coefficients are 7, -5, and 3.

How do you simplify algebraic expressions with fractions like 1/2x + 3/2x + 2?

To simplify, group the like terms with x, add their coefficients (1/2 + 3/2 = 4/2), which equals 2. Therefore, 4/2x + 2 simplifies to 2x + 2.

How do you simplify expressions using the distributive property, such as 3(x + 1) + 5x - 4?

First, use the distributive property: multiply 3 by both x and 1 to get 3x + 3. Then, add the remaining terms: 3x + 3 + 5x - 4. Finally, group the like terms (3x + 5x) and (3 - 4) to get 8x - 1.

Simplify Algebraic Expressions with Like Terms | Grade 6 Math Practice & Solutions

Review: Like Terms and Simplifying

In an algebraic expression, like terms are all terms with the same variable raised to the same powers.

Examples: Like Terms

1) \( 2x , \; 4x , \; x , \; \text{and } 10x \) are all like terms with coefficients \( 2, \; 4, \; 1, \; \text{and } 10 \) respectively. The power of the variable \( x \) must be the same.

2) In the algebraic expression: \[ 2x + 7x - 6 + 4x^{2} - 6x \], the terms \( 2x, \; 7x, \; \text{and } -6x \) are all like terms (power of 1). Note that \( 4x^2 \) is not a like term.

Like terms can be added and subtracted by adding their coefficients.

Examples: Simplifying Algebraic Expressions

3) Simplify: \( 3x + 10 + 5x - 6x - 4 \)

Group like terms: \( = (3x + 5x - 6x) + (10 - 4) \)

Factor out the variable: \( = (3 + 5 - 6)x + (10 - 4) = 2x + 6 \)

4) Use distributive property to simplify: \( 2(x - 3) + 3(x + 1) \)

Expand: \( 2x - 6 + 3x + 3 \)

Group like terms: \( = (2x + 3x) + (-6 + 3) = 5x - 3 \)

Solve the following questions

Question 1

What are the like terms and their coefficients in each of the following expressions?

\( 7x - 5x + 6 + 3x \)
\( 6x + 11x + 9 + x - 7 \)
\( 3x + 9y + 9x - y \)
\( \frac{1}{3}x + \frac{2}{3}x - 3 \)

View Solutions

\( 7x, -5x, 3x \) are like terms. Coefficients: \( 7, -5, 3 \).
\( 6x, 11x, x \) are like terms (coefficients \( 6, 11, 1 \)); \( 9 \) and \( -7 \) are like terms.
\( 3x, 9x \) (coefficients \( 3, 9 \)) and \( 9y, -y \) (coefficients \( 9, -1 \)).
\( \frac{1}{3}x \) and \( \frac{2}{3}x \) are like terms. Coefficients: \( \frac{1}{3}, \frac{2}{3} \).

Question 2

Simplify the following expressions:

\( 2x + x \)
\( 12x - 5x + 11 - 4x \)
\( 9x + 11x + 19 - x - 7 \)
\( 4x + 8y + 10x - 3y \)
\( x + 5 + 3y + 6x - x - 2y + 6 \)
\( \frac{1}{2}x + \frac{3}{2}x + 2 \)

View Solutions

\( (2+1)x = 3x \)
\( (12-5-4)x + 11 = 3x + 11 \)
\( (9+11-1)x + (19-7) = 19x + 12 \)
\( (4+10)x + (8-3)y = 14x + 5y \)
\( (1+6-1)x + (3-2)y + (5+6) = 6x + y + 11 \)
\( (\frac{1}{2} + \frac{3}{2})x + 2 = \frac{4}{2}x + 2 = 2x + 2 \)

Question 3

Simplify and identify the equivalent expressions:

\( 3x + 3 + 4x + 2 \)
\( 4x + 2a + 6x + 6a \)
\( x + 2 + 3x + 3x + 3 \)
\( x - x + 3y \)
\( 7a + 10x + a \)
\( 4x + 3y - 4x \)

View Solutions

Simplified forms:

a) \( 7x + 5 \)
b) \( 10x + 8a \)
c) \( 7x + 5 \)
d) \( 3y \)
e) \( 10x + 8a \)
f) \( 3y \)

Equivalent: (a & c), (b & e), (d & f).

Question 4

Use the distributive property then simplify:

\( 3(x + 1) + 5x - 4 \)
\( 3(x - 1) + 2(x + 2) + 5x \)
\( 4(x + 2) + 2(y + 2) + x + 3y \)
\( 3(\frac{x}{3} + 1) + 2(\frac{x}{2} - 1) + 3 \)

View Solutions

\( 3x + 3 + 5x - 4 = (3+5) x + (3 - 4) = 8x - 1 \)
\( 3x - 3 + 2x + 4 + 5x = (3+2+5)x + (-3+4) = 10x + 1 \)
\( 4x + 8 + 2y + 4 + x + 3y = (4+1)x + (2+3)y + (8+4) = 5x + 5y + 12 \)
\( (x + 3) + (x - 2) + 3 = (1+1)x + (3 - 2 + 3) = 2x + 4 \)

Simplify Algebraic Expressions Using Like Terms - Grade 6

Review: Like Terms and Simplifying

Examples: Like Terms

Examples: Simplifying Algebraic Expressions

Solve the following questions

Question 1

Question 2

Question 3

Question 4

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