Middle Years

# 7.04 Methods for solving two-step equations

Worksheet
Flow charts and operations
1

The flow chart shows operations being performed on s:

\begin{array}{ccccc} & {-7} & & {\times 6} & \\ s & \to & ⬚ & \to & ⬚ \end{array}

Complete the flow chart.

2

The flow chart shows operations being performed on t:

\begin{array}{ccccc} & +3 & & \div 5 & \\ t & \to & ⬚ & \to & ⬚ \end{array}

Complete the flow chart.

3

Complete the following flow charts to form new expressions:

a
\begin{array}{ccccc} & {\times 5} & & {+8} & \\ y & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
b
\begin{array}{ccccc} & \div 3 & & -7 & \\ k & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
c
\begin{array}{ccccc} & +15 & & \times 8 & \\ p & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
d
\begin{array}{ccccc} & {+5} & & {\div3} & \\ n & \to & ⬚ & \to & ⬚ \\\\ \end{array}
e
\begin{array}{ccccc} & \times 4 & & +3 & \\ x & \to & ⬚ & \to & ⬚ \\\\ \end{array}
f
\begin{array}{ccccc} & {\div 9} & & {-7} & \\ j & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
g
\begin{array}{ccccc} & +28 & & \times 3 & \\ p & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
h
\begin{array}{ccccc} & -6 & & \times 7 & \\ s & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
Operations in reverse order
4

Complete the following flow charts to backtrack to the pronumeral in each expression:

a
\begin{array}{ccccc} & -9 & & \div 6 & \\ 6y+9 & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
b
\begin{array}{ccccc} & \div 5 & & -3 & \\ 5 \left(q + 3\right) & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
c
\begin{array}{ccccc} & \div 6 & & +9 & \\ 6 \left(s - 9\right) & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
d
\begin{array}{ccccc} & \times 5 & & -8 & \\ \dfrac{n + 8}{5} & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
e
\begin{array}{ccccc} & +6 & & \times 5 & \\ \dfrac{j}{5}-6 & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
f
\begin{array}{ccccc} & -9 & & \div 8 & \\ 8y+9 & \to & ⬚ & \to & ⬚ \\ \\ \end{array}
5

Complete the following flow charts by identifying the required operations:

a
\begin{array}{ccccc} & ⬚ & & ⬚ & \\ 4 \left(q + 9\right) & \to & q + 9 & \to & q \\ \\ \end{array}
b
\begin{array}{ccccc} & ⬚ & & ⬚ & \\ 5 \left(r - 7\right) & \to & r-7 & \to & r \\ \\ \end{array}
c
\begin{array}{ccccc} & ⬚ & & ⬚ & \\ \dfrac{n + 6}{9} & \to & n+6 & \to & n \\ \\ \end{array}
d
\begin{array}{ccccc} & ⬚ & & ⬚ & \\ \dfrac{j}{2}-7 & \to & \dfrac{j}{2} & \to & j \\ \\ \end{array}
Two-step equations
6

Consider the equation 4 x + 16 = 24.

a

Identify which operations should be done to make x the subject of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ 4x + 16&\to&4x&\to&x \end{array}

b

Complete the following flow chart by applying the same operations to the right-hand side of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ 24&\to&⬚&\to&⬚ \end{array}

c

Hence, find the value of x that will make the equation true.

7

Consider the equation 3 \left(p + 11\right) = 57.

a

Identify which operations should be done to make p the subject of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ 3 \left(p + 11\right)&\to&p + 11&\to&p \end{array}

b

Complete the following flow chart by applying the same operations to the right-hand side of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ 57&\to&⬚&\to&⬚ \end{array}

c

Hence, find the value of p that will make the equation true.

8

Consider the equation \dfrac{j}{7} - 11 = - 7.

a

Identify which operations should be done to make s the subject of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ \dfrac{j}{7} - 11&\to&\dfrac{j}{7}&\to&j \end{array}

b

Complete the following flow chart by applying the same operations to the right-hand side of the equation:\begin{array}{ccccc} &\text{Operation }1&&\text{Operation }2&\\ -7&\to&⬚&\to&⬚ \end{array}

c

Hence, find the value of s that will make the equation true.

9
For each of the following equations:
i

Describe the operations required to make the pronumeral the subject.

ii

Hence, solve the equation.

a
7 p + 6 = 41
b
2 x - 5 = 11
c
5 \left(n - 15\right) = 35
d
10 \left(p + 10\right) = 120
e
\dfrac{y}{8} + 3 = 5
f
\dfrac{x}{3} - 11 = 9
g
\dfrac{u + 22}{6} = 4
h
\dfrac{y - 10}{2} = 5