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 \(-\frac{9}{7} n+1\).