Simplifying Algebraic Expressions

1. Combine the like terms to create an equivalent expression: $−n+(−4)−(−4n)+6$

2. Combine the like terms to create an equivalent expression: $-2 x-x+8$

3. Combine the like terms to create an equivalent expression: $2 s+(-4 s)$

4. Combine the like terms to create an equivalent expression: $-3 x-6+(-1)$

5. Combine the like terms to create an equivalent expression: $2 r+1+(-4 r)+7$

6 . Combine the like terms to create an equivalent expression: $−5r+8r+5$

7. Combine the like terms to create an equivalent expression: $r+(−5r)$

1. Combine the $n$ terms:

$\begin{aligned} -n+(-4)-(-4 n)+6 &=(-1+4) n-4+6 \\ &=3 n-4+6 \end{aligned}$

Combine the numeric terms:

$3 n-4+6=3 n+2$

The simplified expression is $3n + 2$.

2. Combine the $x$ terms:

$\begin{aligned} -2 x-x+8 &=(-2-1) x+8 \\ &=-3 x+8 \end{aligned}$

The simplified expression is $-3x + 8$.

3. Combine the $s$ terms:

$\begin{aligned} 2 s+(-4 s) &=(2-4) s \\ &=-2 s \end{aligned}$

The simplified expression is $-2s$.

4. Combine the numeric terms:

$-3 x-6-1=-3 x-7$

The simplified expression is $-3x - 7$.

5. Combine the $r$ terms:

$\begin{aligned} 2 r+1+(-4 r)+7 &=(2-4) r+1+7 \\ &=-2 r+1+7 \end{aligned}$

Combine the numeric terms:

$−2r+1+7=−2r+8$

The simplified expression is $-2r +8$.

6. Combine the $r$ terms:

$\begin{aligned} -5 r+8 r+5 &=(-5+8) r+5 \\ &=3 r+5 \end{aligned}$

The simplified expression is $3r + 5$.

7. Combine the $r$ terms:

$\begin{aligned} r+(-5 r) &=(1-5) r \\ &=-4 r \end{aligned}$

The simplified expression is $-4r$.

1. Simplify to create an equivalent expression. $2(−2−4p)+2(−2p−1)$

Choose 1 answer:

A. $−12p−6$

B. $-10p - 6$

C. $-12p+6$

D. $12p-6$

2. Simplify to create an equivalent expression. $1+4(6p−9)$

Choose 1 answer:

A. $6p−35$

B. $24p−35$

C. $24p−36$

D. $6p−36$

3. Simplify to create an equivalent expression. $4(−15−3p)−4(−p+5)$

A. $−8p−80$

B. $−13p−80$

C. $−8p+80$

D. $8p-80$

4. Simplify to create an equivalent expression. $2−4(5p+1)$

A. $−20p−2$

B. $−5p−4$

C. $−20p+2$

D. $−5p+4$

1. A. $−12p−6$

2. B. $24p−35$

3. A. $−8p−80$

4. A. $−20p−2$

1. Combine like terms to create an equivalent expression. $−2.5(4x−3)$

2. Combine like terms to create an equivalent expression. $1.3b+7.8−3.2b$

3. Combine like terms to create an equivalent expression. $-\frac{2}{3} p+\frac{1}{5}-1+\frac{5}{6} p$
Enter any coefficients as simplified proper or improper fractions or integers.

4. Combine like terms to create an equivalent expression. $\frac{1}{7}-3\left(\frac{3}{7} n-\frac{2}{7}\right)$
Enter any coefficients as simplified proper or improper fractions or integers.

1. Use the distributive property to multiply the $-2.5$ into the parentheses.

= $−2.5(4x−3)$

= $−2.5⋅(4x)+(−2.5)⋅(−3)$

We expanded the expression by multiplying the $-2.5$ by both terms in the parentheses.

=$-10x+7.5$

The expanded expression is $-10x+7.5$.

2. Combine the coefficients of the $b$ terms.

= $=1.3b+7.8−3.2b$

= $(1.3−3.2)⋅b+7.8$

= $(−1.9)⋅b+7.8$

= $−1.9b+7.8$

The simplified expression is $−1.9b+7.8$.

3. Combine the coefficients of the $p$ terms, and combine the constant terms.

= $-\frac{2}{3} p+\frac{1}{5}-1+\frac{5}{6} p$

= $\left(-\frac{2}{3}+\frac{5}{6}\right) \cdot p+\frac{1}{5}-1$

Group the $p$ coefficients together, and group the numeric coefficients together.

= $\left(-\frac{4}{6}+\frac{5}{6}\right) \cdot p+\frac{1}{5}-\frac{5}{5}$

Rewrite $−1$ as $-\frac{5}{5}$ to form common denominators.

= $\left(\frac{1}{6}\right) \cdot p-\frac{4}{5}$

=$\frac{1}{6} p-\frac{4}{5}$

The simplified expression is $\frac{1}{6} p-\frac{4}{5}$.

4. Use the distributive property to multiply the $-3$ into the parentheses.

= $\frac{1}{7}-3\left(\frac{3}{7} n-\frac{2}{7}\right)$

= $\frac{1}{7}+(-3) \cdot\left(\frac{3}{7} n\right)+(-3) \cdot\left(-\frac{2}{7}\right)$

We expanded the expression by multiplying the $-3$ by both terms in the parentheses.

= $\frac{1}{7}-\frac{9}{7} n+\frac{6}{7}$

= $-\frac{9}{7} n+\frac{7}{7}$

We combined the numeric terms.

= $-\frac{9}{7} n+1$

The expanded expression is $-\frac{9}{7} n+1$.