Combine Like Terms
Simplify:
4x + 3x
7x
Expand:
3 (x + 2)
3x + 6
Are 3x + 5 and 5 + 3x equivalent? Why?
Yes, Commutative Property.
Rewrite x + x + x + x using multiplication.
4x
A student says: 2x + 3x = 5x2. What is the mistake? What is the correct answer?
They should add coefficients, not multiply the variable factors. The correct answer is 5x.
Simplify:
8a + 5 - 3a
5a + 5
Expand:
5 (2x - 3)
10x - 15
Are 4 (x + 2) and 4x + 2 equivalent?
No, the first simplifies to 4x + 8.
Rewrite 7a + 14 using the Distributive Property.
7 (a + 2)
A student expands: 3 (x + 5) as 3x + 5. What is the correct answer?
3x + 15
Simplify:
6x + 4 - 2x + 9
4x + 13
Expand:
-2 (x + 4)
-2x - 8
Are 6x - 2x and 4x equivalent?
Yes, both simplify to 4x.
Rewrite 12x - 18 by factoring out the greatest common factor.
6 (2x - 3)
A student simplifies: 8x - 3x + 2 as 5 (x + 2). Is this correct? If not, what is the correct expression?
No, the correct expression is 5x + 2.
Simplify:
7y - 3 + 2y - 8
9y - 11
Expand:
4 (3x - 2) + 5
12x - 3
Are 2 (x + 3) + x and 3x + 6 equivalent?
Yes, both simplify to 3x + 6.
Write an expression equivalent to 3 (x + 4) + 2x.
5x + 12
A student says: -4 (x - 2) = -4x - 8. What is the correct answer?
-4x + 8. Multiplying two negative numbers gives a positive product.
Simplify:
5x + 3 - 2x + 7 - 4x
-x + 10
Expand:
3 (2x - 5) - 2 (x + 4)
4x - 23
Are 5 (x - 2) and 5x - 2 equivalent?
No, the first simplifies to 5x - 10, while the second is 5x - 2.
Write an expression equivalent to 4 ( 2x - 3) - 3 (x + 5).
5x - 27
A student claims: 2 (3x + 4) - x = 5x + 4. Find the correct result.
6x + 8 - x = 5x + 8