Question

5.2 distributing & combining like terms practice
directions: distribute, then combine like terms to simplify each expression below!

expression	simplified expression
2. $-7(x + 2)-x + 1$
3. $3x + 4-2(x + 10)-y + 80 + 5y$
4. $-(9 - 6x)+\frac{1}{2}-8(x+\frac{1}{4})$
5. $5(y + 11x)-13 + 7$
6. $3x + 4-x(2 + 10)$

Explanation:

Step1: Distribute in 2(3x + 4)

$2\times3x+2\times4 - 2x+10=6x + 8-2x + 10$

Step2: Combine like - terms

$(6x-2x)+(8 + 10)=4x+18$

Step1: Distribute in - 7(x + 2)

$-7x-7\times2-x + 1=-7x-14-x + 1$

Step2: Combine like - terms

$(-7x-x)+(-14 + 1)=-8x-13$

Step1: Distribute in - 2(x + 10)

$3x + 4-2x-2\times10-y + 80+5y=3x + 4-2x-20-y + 80+5y$

Step2: Combine like - terms

$(3x-2x)+(4-20 + 80)+(-y + 5y)=x + 64+4y$

Step1: Distribute in -(9 - 6x) and - 8(x + 1/4)

$-9 + 6x+\frac{1}{2}-8x-8\times\frac{1}{4}=-9 + 6x+\frac{1}{2}-8x - 2$

Step2: Combine like - terms

$(6x-8x)+(-9+\frac{1}{2}-2)=-2x+(-9 - 2+\frac{1}{2})=-2x+(-11+\frac{1}{2})=-2x-\frac{22 - 1}{2}=-2x-\frac{21}{2}$

Answer:

$4x + 18$