Solve for x x+2(3x-1)=0
The problem presented is an algebraic equation that asks to find the value(s) of the variable x that make the equation true. Specifically, the equation is a linear equation where x is to be isolated and its value determined by applying algebraic rules to simplify the equation and solve for x.
$x + 2 \left(\right. 3 x - 1 \left.\right) = 0$
Answer
Solution:
Step:1
Expand the expression $x + 2(3x - 1)$.
Step:1.1
Break down the expression term by term.
Step:1.1.1
Utilize the distributive property to expand: $x + 2(3x) + 2(-1) = 0$
Step:1.1.2
Perform the multiplication of $2$ and $3$: $x + 6x + 2(-1) = 0$
Step:1.1.3
Multiply $2$ by $-1$: $x + 6x - 2 = 0$
Step:1.2
Combine like terms $x$ and $6x$: $7x - 2 = 0$
Step:2
Isolate the variable term by adding $2$ to both sides: $7x = 2$
Step:3
Divide the equation $7x = 2$ by $7$ to solve for $x$.
Step:3.1
Divide each side of the equation by $7$: $\frac{7x}{7} = \frac{2}{7}$
Step:3.2
Simplify the equation.
Step:3.2.1
Eliminate the common factor of $7$.
Step:3.2.1.1
Reduce the fraction by canceling out $7$: $\frac{\cancel{7}x}{\cancel{7}} = \frac{2}{7}$
Step:3.2.1.2
Simplify to find $x$: $x = \frac{2}{7}$
Step:4
Express the solution in various formats.
Exact Form: $x = \frac{2}{7}$
Decimal Form: $x \approx 0.2857$
Knowledge Notes:
To solve the given equation $x + 2(3x - 1) = 0$, we follow a systematic approach:
Distributive Property: This property states that $a(b + c) = ab + ac$. We apply this to expand the expression $2(3x - 1)$.
Combining Like Terms: Terms that contain the same variable to the same power are combined by adding or subtracting their coefficients.
Isolation of the Variable: To solve for $x$, we need to get $x$ on one side of the equation by itself. This involves undoing any addition or subtraction around $x$ and then any multiplication or division.
Simplification: After isolating the variable, we simplify the equation by performing arithmetic operations such as division to find the value of $x$.
Fraction Reduction: When we have a fraction, we look for common factors in the numerator and denominator to reduce the fraction to its simplest form.
Solution Representation: The solution can be presented in different forms, such as an exact fraction or a decimal approximation. The decimal form can be obtained using a calculator or long division.
