#### xaktly | Algebra | ax + b = c

Algebra practice 1

### Solving problems of the type   $ax + b = c$

This is one of the simplest kinds of algebra problems and a good introduction to solving for x. Here's an example:

$$4x + 5 = 7$$

To solve it, we need to work on it until it's in the form $x = c,$ where c is our solution. To do that, consider that x has two things "stuck" to it that we'll have to remove – but by the rules. The first is the added 5 and the second is the multiplied 4.

The easiest thing to get rid of is the 5 (pick the low-hanging fruit). Do that by subtracting it from both sides (because it's added on the left and we use inverse operations).

\begin{align} & 4x + 5 = 7 \\ &\underline{\phantom{00} -5 -5}\\ &\phantom{000} 4x = 7 \end{align}

Now we just need to move the 4 over by division:

$$\frac{4x}{4} = \frac{7}{4} \longrightarrow \bf x = \frac{7}{4}$$

You can practice problems of this type below. Follow the steps and enter your answer as an integer a fraction of integers, like 3/4, or a decimal number like 1.55. Do as many problems as you need to get good at these. You'll form a solid foundation for what comes next.

Next we'll add some rational fractions like $\frac{2}{5}$ to complicate things a little more. Fractions are your friends!

#### Inverse operations

In this section, we'll refer often to inverse operations. Inverse operations are opposite, and one can be used to undo the action of the other.

• Addition and subtraction are inverse operations.

• Multiplication and division are inverse operations.

#### Other Algebra practice problems

There are a number of these pages you can use for algebra practice. Just pick the rough type of problem you need to work on.

Type 1:   $ax + by = c$

Type 2:   $\frac{a}{b}x + \frac{c}{d} = \frac{e}{f}$

Type 3:   $\frac{a}{x} + b = c$

Type 4:   $\frac{a}{x} + \frac{b}{c} = \frac{d}{e}$

Type 5:   $ax^2 + b = c$

Type 6:   $ax^2 + \frac{b}{c} = \frac{d}{e}$

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