Solved on Jan 19, 2024

Solve for $x$ in the equation $x-4=-2x+9$ . Round to the nearest tenth if necessary.

STEP 1

Assumptions
1. We are given the linear equation $x - 4 = -2x + 9$ .
2. We need to solve for $x$ .
3. If rounding is necessary, we round to the nearest tenth.

STEP 2

First, we will collect like terms by moving all terms involving $x$ to one side of the equation and constants to the other side. We can do this by adding $2x$ to both sides of the equation to move the $x$ -terms to the left side.
$x - 4 + 2x = -2x + 9 + 2x$

STEP 3

Combine like terms on both sides of the equation.
$3x - 4 = 9$

STEP 4

Next, we will isolate $x$ by moving the constant term on the left side to the right side. We can do this by adding $4$ to both sides of the equation.
$3x - 4 + 4 = 9 + 4$

STEP 5

Simplify both sides of the equation.
$3x = 13$

STEP 6

Now, we will solve for $x$ by dividing both sides of the equation by the coefficient of $x$ , which is $3$ .
$\frac{3x}{3} = \frac{13}{3}$

STEP 7

Simplify the equation to find the value of $x$ .
$x = \frac{13}{3}$

STEP 8

Calculate the decimal value of $x$ and round to the nearest tenth if necessary.
$x \approx 4.3$
The solution for $x$ is approximately $4.3$ when rounded to the nearest tenth.

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Solve for $x$ in the equation $x-4=-2x+9$ . Round to the nearest tenth if necessary.

STEP 1

Assumptions
1. We are given the linear equation $x - 4 = -2x + 9$ .
2. We need to solve for $x$ .
3. If rounding is necessary, we round to the nearest tenth.

STEP 2

First, we will collect like terms by moving all terms involving $x$ to one side of the equation and constants to the other side. We can do this by adding $2x$ to both sides of the equation to move the $x$ -terms to the left side.
$x - 4 + 2x = -2x + 9 + 2x$

STEP 3

Combine like terms on both sides of the equation.
$3x - 4 = 9$

STEP 4

Next, we will isolate $x$ by moving the constant term on the left side to the right side. We can do this by adding $4$ to both sides of the equation.
$3x - 4 + 4 = 9 + 4$

STEP 5

Simplify both sides of the equation.
$3x = 13$

STEP 6

Now, we will solve for $x$ by dividing both sides of the equation by the coefficient of $x$ , which is $3$ .
$\frac{3x}{3} = \frac{13}{3}$

STEP 7

Simplify the equation to find the value of $x$ .
$x = \frac{13}{3}$

STEP 8

Calculate the decimal value of $x$ and round to the nearest tenth if necessary.
$x \approx 4.3$
The solution for $x$ is approximately $4.3$ when rounded to the nearest tenth.

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Solve for xxx in the equation x−4=−2x+9x-4=-2x+9x−4=−2x+9. Round to the nearest tenth if necessary.

STEP 1

Assumptions1. We are given the linear equation x−4=−2x+9 x - 4 = -2x + 9 x−4=−2x+9.2. We need to solve for x x x.3. If rounding is necessary, we round to the nearest tenth.

STEP 2

STEP 3

Combine like terms on both sides of the equation.3x−4=9 3x - 4 = 9 3x−4=9

STEP 4

Next, we will isolate x x x by moving the constant term on the left side to the right side. We can do this by adding 4 4 4 to both sides of the equation.3x−4+4=9+4 3x - 4 + 4 = 9 + 4 3x−4+4=9+4

STEP 5

Simplify both sides of the equation.3x=13 3x = 13 3x=13

STEP 6

Now, we will solve for x x x by dividing both sides of the equation by the coefficient of x x x, which is 3 3 3.3x3=133 \frac{3x}{3} = \frac{13}{3} 33x​=313​

STEP 7

Simplify the equation to find the value of x x x.x=133 x = \frac{13}{3} x=313​

STEP 8

Calculate the decimal value of x x x and round to the nearest tenth if necessary.x≈4.3 x \approx 4.3 x≈4.3The solution for x x x is approximately 4.3 4.3 4.3 when rounded to the nearest tenth.

Start learning now

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

Solve for $x$ in the equation $x-4=-2x+9$ . Round to the nearest tenth if necessary.

Assumptions
1. We are given the linear equation $x - 4 = -2x + 9$ .
2. We need to solve for $x$ .
3. If rounding is necessary, we round to the nearest tenth.

Combine like terms on both sides of the equation.
$3x - 4 = 9$

Next, we will isolate $x$ by moving the constant term on the left side to the right side. We can do this by adding $4$ to both sides of the equation.
$3x - 4 + 4 = 9 + 4$

Simplify both sides of the equation.
$3x = 13$

Now, we will solve for $x$ by dividing both sides of the equation by the coefficient of $x$ , which is $3$ .
$\frac{3x}{3} = \frac{13}{3}$

Simplify the equation to find the value of $x$ .
$x = \frac{13}{3}$

Calculate the decimal value of $x$ and round to the nearest tenth if necessary.
$x \approx 4.3$
The solution for $x$ is approximately $4.3$ when rounded to the nearest tenth.