Question4. $0.8+0.3(2-3 x)=1.4$

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 $x$ .
3. Basic algebraic operations will be used, including distribution, addition, subtraction, and division.

STEP 2

1. Simplify the equation by distributing the constant within the parentheses.
2. Combine like terms and isolate the term containing $x$ .
3. Solve for $x$ by performing algebraic operations.
4. Check the solution by substituting it back into the original equation.

STEP 3

Distribute $0.3$ across the terms inside the parentheses:
$0.8 + 0.3 \times 2 - 0.3 \times 3x = 1.4$
Simplify the distribution:
$0.8 + 0.6 - 0.9x = 1.4$

STEP 4

Combine the constant terms on the left side of the equation:
$1.4 - 0.9x = 1.4$
Subtract $1.4$ from both sides to isolate the term with $x$ :
$-0.9x = 0$

STEP 5

Divide both sides by $-0.9$ to solve for $x$ :
$x = \frac{0}{-0.9}$
Simplify the division:
$x = 0$

STEP 6

Check the solution by substituting $x = 0$ back into the original equation:
$0.8 + 0.3(2 - 3 \times 0) = 1.4$
Simplify the expression:
$0.8 + 0.3 \times 2 = 1.4$
$0.8 + 0.6 = 1.4$
$1.4 = 1.4$
The left-hand side equals the right-hand side, confirming the solution is correct.
The solution is:
$\boxed{0}$

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