Question $-0.8+0.3(2-3 x)=1.4$

Studdy Solution

STEP 1

1. The equation $-0.8 + 0.3(2 - 3x) = 1.4$ is a linear equation in one variable, $x$ .
2. The goal is to solve for $x$ by isolating it on one side of the equation.
3. Basic algebraic operations, including distribution and combining like terms, will be used.

STEP 2

1. Simplify the equation by distributing and combining like terms.
2. Isolate the variable $x$ by performing algebraic operations.
3. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $0.3$ across the terms inside the parentheses:
$-0.8 + 0.3 \times 2 - 0.3 \times 3x = 1.4$
Simplify the distribution:
$-0.8 + 0.6 - 0.9x = 1.4$
Combine the constant terms on the left-hand side:
$-0.2 - 0.9x = 1.4$

STEP 4

To isolate $x$ , first add $0.2$ to both sides of the equation:
$-0.9x = 1.4 + 0.2$
Simplify the right-hand side:
$-0.9x = 1.6$

STEP 5

Next, divide both sides by $-0.9$ to solve for $x$ :
$x = \frac{1.6}{-0.9}$
Simplify the division:
$x \approx -1.7778$

STEP 6

Check the solution by substituting $x \approx -1.7778$ back into the original equation:
$-0.8 + 0.3(2 - 3(-1.7778)) \approx 1.4$
Calculate the expression inside the parentheses:
$2 + 5.3334 \approx 7.3334$
Calculate the entire left-hand side:
$-0.8 + 0.3 \times 7.3334 \approx -0.8 + 2.2 \approx 1.4$
Both sides are approximately equal, confirming the solution.
The solution is:
$x \approx -1.7778$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms