# Solving two-step linear equations: $ax + b = c$, ${x \over a} + b = c$

### Solving two-step linear equations: $ax + b = c$, ${x \over a} + b = c$

Solving two-step linear equations literally means solving the equations in two major steps. First, we need to isolate the unknown "x" to one side of the equation. You can then solve the "x". To complete these two steps, you may need to perform addition, subtraction, division, multiplication, cross multiplication, and so on. When the equation has fractions, you may also need to find the common denominator before proceeding further. Seems complicated? No worries! You will learn all the tricks in this section.

#### Lessons

• Introduction
a)
How to turn a word problem into an equation?
• ex. 1: "revenue" problem
• ex. 2: "area" problem

• 1.
Solve.
a)
$\frac{4}{5} + \frac{5}{4}x = \frac{1}{3}$

b)
$\frac{3}{4} + 2x = 5\frac{1}{3}$

c)
$\frac{2}{3} - \frac{x}{2} = \frac{4}{7}$

d)
$- 3\frac{3}{4} = - 6\frac{1}{4} + \frac{1}{8}x$

• 2.
Solve.
a)
$- 0.05 - \frac{x}{{2.6}} = - 0.03$

b)
$\frac{x}{{ - 2.14}} + 0.86 = 6.32$

• 3.
Solve.
a)
$3.07 = 0.3x - 4.6$

b)
$\frac{7}{9} = \frac{7}{8} - \frac{x}{9}$

c)
$- 1.8 = 4.5 + \frac{x}{{2.3}}$

d)
$3\frac{1}{3} + 2\frac{1}{9}v = - \frac{4}{9}$

• 4.
The number of hours Peter exercised in May is 3.5 hours less than one fourth of the number of hours John exercised in the same month. Peter had 15.8 hours of exercise in May. How many hours of exercise did John have in May?