Solved on Jan 23, 2024

Solve the equation $3(2x+1) = 2x-1$ , showing all work.

STEP 1

Assumptions
1. We are given the linear equation $3(2x + 1) = 2x - 1$ .
2. We will solve for $x$ by applying algebraic principles such as the distributive property, combining like terms, and isolating the variable.

STEP 2

First, we will apply the distributive property to the left side of the equation to eliminate the parentheses.
$3(2x + 1) = 2x - 1$
$3 \cdot 2x + 3 \cdot 1 = 2x - 1$

STEP 3

Perform the multiplication on the left side of the equation.
$6x + 3 = 2x - 1$

STEP 4

Now, we will move all terms containing $x$ to one side of the equation and the constant terms to the other side. We do this by subtracting $2x$ from both sides of the equation to get the $x$ -terms on one side.
$6x + 3 - 2x = 2x - 1 - 2x$

STEP 5

Combine like terms on both sides of the equation.
$6x - 2x + 3 = -1$

STEP 6

Simplify the equation by combining the $x$ -terms.
$4x + 3 = -1$

STEP 7

Next, we will isolate the $x$ -term by subtracting 3 from both sides of the equation to move the constant term to the other side.
$4x + 3 - 3 = -1 - 3$

STEP 8

Simplify the equation by performing the subtraction.
$4x = -4$

STEP 9

To find the value of $x$ , we will divide both sides of the equation by 4, which is the coefficient of $x$ .
$\frac{4x}{4} = \frac{-4}{4}$

STEP 10

Simplify both sides of the equation to solve for $x$ .
$x = -1$
The solution to the equation $3(2x + 1) = 2x - 1$ is $x = -1$ .

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Solve the equation $3(2x+1) = 2x-1$ , showing all work.

STEP 1

Assumptions
1. We are given the linear equation $3(2x + 1) = 2x - 1$ .
2. We will solve for $x$ by applying algebraic principles such as the distributive property, combining like terms, and isolating the variable.

STEP 2

First, we will apply the distributive property to the left side of the equation to eliminate the parentheses.
$3(2x + 1) = 2x - 1$
$3 \cdot 2x + 3 \cdot 1 = 2x - 1$

STEP 3

Perform the multiplication on the left side of the equation.
$6x + 3 = 2x - 1$

STEP 4

Now, we will move all terms containing $x$ to one side of the equation and the constant terms to the other side. We do this by subtracting $2x$ from both sides of the equation to get the $x$ -terms on one side.
$6x + 3 - 2x = 2x - 1 - 2x$

STEP 5

Combine like terms on both sides of the equation.
$6x - 2x + 3 = -1$

STEP 6

Simplify the equation by combining the $x$ -terms.
$4x + 3 = -1$

STEP 7

Next, we will isolate the $x$ -term by subtracting 3 from both sides of the equation to move the constant term to the other side.
$4x + 3 - 3 = -1 - 3$

STEP 8

Simplify the equation by performing the subtraction.
$4x = -4$

STEP 9

To find the value of $x$ , we will divide both sides of the equation by 4, which is the coefficient of $x$ .
$\frac{4x}{4} = \frac{-4}{4}$

STEP 10

Simplify both sides of the equation to solve for $x$ .
$x = -1$
The solution to the equation $3(2x + 1) = 2x - 1$ is $x = -1$ .

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Solve the equation 3(2x+1)=2x−13(2x+1) = 2x-13(2x+1)=2x−1, showing all work.

STEP 1

Assumptions1. We are given the linear equation 3(2x+1)=2x−13(2x + 1) = 2x - 13(2x+1)=2x−1.2. We will solve for xxx by applying algebraic principles such as the distributive property, combining like terms, and isolating the variable.

STEP 2

First, we will apply the distributive property to the left side of the equation to eliminate the parentheses.3(2x+1)=2x−13(2x + 1) = 2x - 13(2x+1)=2x−13⋅2x+3⋅1=2x−13 \cdot 2x + 3 \cdot 1 = 2x - 13⋅2x+3⋅1=2x−1

STEP 3

Perform the multiplication on the left side of the equation.6x+3=2x−16x + 3 = 2x - 16x+3=2x−1

STEP 4

Now, we will move all terms containing xxx to one side of the equation and the constant terms to the other side. We do this by subtracting 2x2x2x from both sides of the equation to get the xxx-terms on one side.6x+3−2x=2x−1−2x6x + 3 - 2x = 2x - 1 - 2x6x+3−2x=2x−1−2x

STEP 5

Combine like terms on both sides of the equation.6x−2x+3=−16x - 2x + 3 = -16x−2x+3=−1

STEP 6

Simplify the equation by combining the xxx-terms.4x+3=−14x + 3 = -14x+3=−1

STEP 7

Next, we will isolate the xxx-term by subtracting 3 from both sides of the equation to move the constant term to the other side.4x+3−3=−1−34x + 3 - 3 = -1 - 34x+3−3=−1−3

STEP 8

Simplify the equation by performing the subtraction.4x=−44x = -44x=−4

STEP 9

To find the value of xxx, we will divide both sides of the equation by 4, which is the coefficient of xxx.4x4=−44\frac{4x}{4} = \frac{-4}{4}44x​=4−4​

STEP 10

Simplify both sides of the equation to solve for xxx.x=−1x = -1x=−1The solution to the equation 3(2x+1)=2x−13(2x + 1) = 2x - 13(2x+1)=2x−1 is x=−1x = -1x=−1.

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Solve the equation $3(2x+1) = 2x-1$ , showing all work.

Assumptions
1. We are given the linear equation $3(2x + 1) = 2x - 1$ .
2. We will solve for $x$ by applying algebraic principles such as the distributive property, combining like terms, and isolating the variable.

First, we will apply the distributive property to the left side of the equation to eliminate the parentheses.
$3(2x + 1) = 2x - 1$
$3 \cdot 2x + 3 \cdot 1 = 2x - 1$

Perform the multiplication on the left side of the equation.
$6x + 3 = 2x - 1$

Now, we will move all terms containing $x$ to one side of the equation and the constant terms to the other side. We do this by subtracting $2x$ from both sides of the equation to get the $x$ -terms on one side.
$6x + 3 - 2x = 2x - 1 - 2x$

Combine like terms on both sides of the equation.
$6x - 2x + 3 = -1$

Simplify the equation by combining the $x$ -terms.
$4x + 3 = -1$

Next, we will isolate the $x$ -term by subtracting 3 from both sides of the equation to move the constant term to the other side.
$4x + 3 - 3 = -1 - 3$

Simplify the equation by performing the subtraction.
$4x = -4$

To find the value of $x$ , we will divide both sides of the equation by 4, which is the coefficient of $x$ .
$\frac{4x}{4} = \frac{-4}{4}$

Simplify both sides of the equation to solve for $x$ .
$x = -1$
The solution to the equation $3(2x + 1) = 2x - 1$ is $x = -1$ .