Question

5.3 multi - step equations practice
directions: solve each equation below.

	equation	check your answer
2	(-7(x + 2)-x = 2)
3	(3x + 4 - x=-12)
4	(-(9 - 6x)+5=-3)
5	(5(x + 16)=60)
6	(3x + 4 - x(2 + 10)=31)

Explanation:

Step1: Expand and simplify equation 1

\[

$$\begin{align*} 6x + 8-2(3x + 4)-2x&=10\\ 6x + 8-(6x + 8)-2x&=10\\ 6x + 8 - 6x-8-2x&=10\\ -2x&=10 \end{align*}$$

\]

Step2: Solve for x in equation 1

\[x=\frac{10}{-2}=- 5\]

Step3: Expand and simplify equation 2

\[

$$\begin{align*} -7(x + 2)-x&=2\\ -7x-14 - x&=2\\ -8x-14&=2 \end{align*}$$

\]

Step4: Solve for x in equation 2

\[

$$\begin{align*} -8x&=2 + 14\\ -8x&=16\\ x&=\frac{16}{-8}=-2 \end{align*}$$

\]

Step5: Simplify equation 3

\[

$$\begin{align*} 3x + 4-x&=-12\\ 2x+4&=-12 \end{align*}$$

\]

Step6: Solve for x in equation 3

\[

$$\begin{align*} 2x&=-12 - 4\\ 2x&=-16\\ x&=\frac{-16}{2}=-8 \end{align*}$$

\]

Step7: Expand and simplify equation 4

\[

$$\begin{align*} -(9 - 6x)+5&=-3\\ -9 + 6x+5&=-3\\ 6x-4&=-3 \end{align*}$$

\]

Step8: Solve for x in equation 4

\[

$$\begin{align*} 6x&=-3 + 4\\ 6x&=1\\ x&=\frac{1}{6} \end{align*}$$

\]

Step9: Expand equation 5

\[

$$\begin{align*} 5(x + 16)&=60\\ 5x+80&=60 \end{align*}$$

\]

Step10: Solve for x in equation 5

\[

$$\begin{align*} 5x&=60 - 80\\ 5x&=-20\\ x&=\frac{-20}{5}=-4 \end{align*}$$

\]

Step11: Expand and simplify equation 6

\[

$$\begin{align*} 3x + 4-x(2 + 10)&=31\\ 3x + 4-12x&=31\\ -9x+4&=31 \end{align*}$$

\]

Step12: Solve for x in equation 6

\[

$$\begin{align*} -9x&=31 - 4\\ -9x&=27\\ x&=\frac{27}{-9}=-3 \end{align*}$$

\]

Answer:

1. \(x = - 5\)
2. \(x=-2\)
3. \(x=-8\)
4. \(x=\frac{1}{6}\)
5. \(x=-4\)
6. \(x=-3\)