Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 10, 2023

Solve the equation $4(0.2x - 5) = 12$ . Find all real solutions.

STEP 1

Assumptions
1. We are given the equation $4(0.2x - 5) = 12$ .
2. We need to solve for $x$ .

STEP 2

First, we need to distribute the 4 across the terms inside the parentheses.
$4(0.2x - 5) = 4 \cdot 0.2x - 4 \cdot 5$

STEP 3

Now, perform the multiplication.
$0.8x - 20 = 12$

STEP 4

Next, we need to isolate the term with $x$ on one side. To do this, we add 20 to both sides of the equation.
$0.8x - 20 + 20 = 12 + 20$

STEP 5

Simplify both sides of the equation.
$0.8x = 32$

STEP 6

To find the value of $x$ , we need to divide both sides of the equation by 0.8.
$\frac{0.8x}{0.8} = \frac{32}{0.8}$

STEP 7

Perform the division to solve for $x$ .
$x = 40$
The solution to the equation $4(0.2 x-5)=12$ is $x=40$ .

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