Solving two-step linear equations using addition and subtraction: $ax + b = c$

Lesson: 1a
1:23
Lesson: 1b
1:25
Lesson: 2a
1:34
Lesson: 2b
1:23
Lesson: 3a
1:36
Lesson: 3b
1:29
Lesson: 3c
1:24
Lesson: 3d
1:13
Lesson: 4
1:46

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Solving two-step linear equations using addition and subtraction: $ax + b = c$

In this section, we will look at linear equation questions which involve two kinds of operations: addition and subtraction. We will deal with two-step linear equations modeled by diagrams as a start. Then, we will learn how to solve algebraic equations and related word problems.

Basic concepts: Understanding integer division, Model and solve one-step linear equations:

ax = b

\frac{x}{a} = b

Lessons

1.
Find x in the equation modelled by each diagram.
a)

b)

2.
Find x in the equation modelled by algebra tiles.
a)

b)

3.
Solve.
a)
$7x + 9 = 21$

b)
$98 - 2x = 14$

c)
$- 35 = 6x + 49$

d)
$- 4x - 11 = 109$

4.
The total admission fee of an aquarium for 30 students is $240 after a group discount of $3 for each person. What is the original admission fee before the discount?