Question

solve each equation.

1. $-15 = p - 20$

a) ${-35}$ b) ${5}$
c) ${8}$ d) $left{-\frac{3}{4}
ight}$

1. $34 = -17n$

a) ${-2}$ b) ${17}$
c) ${-12}$ d) ${51}$

1. $3 + \frac{m}{4} = 8$

a) ${-12}$ b) ${10}$
c) ${-8}$ d) ${20}$

1. $-7 - 5x = 28$

a) ${-5}$ b) ${-14}$
c) ${-18}$ d) ${-7}$

1. $21 = n + 6n$

a) ${-3}$ b) ${-13}$
c) ${3}$ d) ${-9}$

1. $3(4b + 6) = 102$

a) ${12}$ b) ${10}$
c) ${7}$ d) ${-9}$

1. $-5(-6 - 6x) = -1 - x$

a) ${10}$ b) ${-5}$
c) ${-1}$ d) ${-11}$

Explanation:

Problem 28:

Step1: Solve for \( p \)

We have the equation \(-15 = p - 20\). To isolate \( p \), we add 20 to both sides of the equation.
\[
-15 + 20 = p - 20 + 20
\]

Step2: Simplify both sides

Simplifying the left side: \(-15 + 20 = 5\). The right side simplifies to \( p \) (since \(-20 + 20 = 0\)). So \( p = 5 \).

Step1: Solve for \( n \)

We have the equation \( 34 = -17n \). To isolate \( n \), we divide both sides by \(-17\).
\[
\frac{34}{-17} = \frac{-17n}{-17}
\]

Step2: Simplify both sides

Simplifying the left side: \(\frac{34}{-17} = -2\). The right side simplifies to \( n \) (since \(\frac{-17n}{-17}=n\)). So \( n = -2 \).

Step1: Isolate the term with \( m \)

We have the equation \( 3+\frac{m}{4}=8 \). Subtract 3 from both sides:
\[
3 - 3+\frac{m}{4}=8 - 3
\]

Step2: Simplify and solve for \( m \)

Simplifying, we get \(\frac{m}{4}=5\). Then multiply both sides by 4:
\[
\frac{m}{4}\times4 = 5\times4
\]
Which gives \( m = 20 \).

Answer:

B) \{5\}

Problem 29: