Solved on Dec 10, 2023

Solve the linear equation $8.6x + 4.4x - 11 = 54$ for the value of $x$ .

STEP 1

Assumptions
1. The equation to solve is $8.6x + 4.4x - 11 = 54$ .
2. We need to find the value of $x$ .

STEP 2

Combine like terms on the left side of the equation. Like terms are terms that contain the same variable raised to the same power.
$8.6x + 4.4x = (8.6 + 4.4)x$

STEP 3

Add the coefficients of $x$ together.
$8.6 + 4.4 = 13.0$

STEP 4

The equation now simplifies to:
$13.0x - 11 = 54$

STEP 5

Add $11$ to both sides of the equation to isolate the term with the variable $x$ on one side.
$13.0x - 11 + 11 = 54 + 11$

STEP 6

Calculate the sum on both sides of the equation.
$13.0x = 65$

STEP 7

Divide both sides of the equation by $13.0$ to solve for $x$ .
$\frac{13.0x}{13.0} = \frac{65}{13.0}$

STEP 8

Calculate the division on both sides to find the value of $x$ .
$x = 5$
The solution to the equation $8.6x + 4.4x - 11 = 54$ is $x = 5$ .

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Solve the linear equation $8.6x + 4.4x - 11 = 54$ for the value of $x$ .

STEP 1

Assumptions
1. The equation to solve is $8.6x + 4.4x - 11 = 54$ .
2. We need to find the value of $x$ .

STEP 2

Combine like terms on the left side of the equation. Like terms are terms that contain the same variable raised to the same power.
$8.6x + 4.4x = (8.6 + 4.4)x$

STEP 3

Add the coefficients of $x$ together.
$8.6 + 4.4 = 13.0$

STEP 4

The equation now simplifies to:
$13.0x - 11 = 54$

STEP 5

Add $11$ to both sides of the equation to isolate the term with the variable $x$ on one side.
$13.0x - 11 + 11 = 54 + 11$

STEP 6

Calculate the sum on both sides of the equation.
$13.0x = 65$

STEP 7

Divide both sides of the equation by $13.0$ to solve for $x$ .
$\frac{13.0x}{13.0} = \frac{65}{13.0}$

STEP 8

Calculate the division on both sides to find the value of $x$ .
$x = 5$
The solution to the equation $8.6x + 4.4x - 11 = 54$ is $x = 5$ .

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Solve the linear equation 8.6x+4.4x−11=548.6x + 4.4x - 11 = 548.6x+4.4x−11=54 for the value of xxx.

STEP 1

Assumptions1. The equation to solve is 8.6x+4.4x−11=548.6x + 4.4x - 11 = 548.6x+4.4x−11=54.2. We need to find the value of xxx.

STEP 2

Combine like terms on the left side of the equation. Like terms are terms that contain the same variable raised to the same power.8.6x+4.4x=(8.6+4.4)x8.6x + 4.4x = (8.6 + 4.4)x8.6x+4.4x=(8.6+4.4)x

STEP 3

Add the coefficients of xxx together.8.6+4.4=13.08.6 + 4.4 = 13.08.6+4.4=13.0

STEP 4

The equation now simplifies to:13.0x−11=5413.0x - 11 = 5413.0x−11=54

STEP 5

Add 111111 to both sides of the equation to isolate the term with the variable xxx on one side.13.0x−11+11=54+1113.0x - 11 + 11 = 54 + 1113.0x−11+11=54+11

STEP 6

Calculate the sum on both sides of the equation.13.0x=6513.0x = 6513.0x=65

STEP 7

Divide both sides of the equation by 13.013.013.0 to solve for xxx.13.0x13.0=6513.0\frac{13.0x}{13.0} = \frac{65}{13.0}13.013.0x​=13.065​

STEP 8

Calculate the division on both sides to find the value of xxx.x=5x = 5x=5The solution to the equation 8.6x+4.4x−11=548.6x + 4.4x - 11 = 548.6x+4.4x−11=54 is x=5x = 5x=5.

Start learning now

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

Solve the linear equation $8.6x + 4.4x - 11 = 54$ for the value of $x$ .

Assumptions
1. The equation to solve is $8.6x + 4.4x - 11 = 54$ .
2. We need to find the value of $x$ .

Combine like terms on the left side of the equation. Like terms are terms that contain the same variable raised to the same power.
$8.6x + 4.4x = (8.6 + 4.4)x$

Add the coefficients of $x$ together.
$8.6 + 4.4 = 13.0$

The equation now simplifies to:
$13.0x - 11 = 54$

Add $11$ to both sides of the equation to isolate the term with the variable $x$ on one side.
$13.0x - 11 + 11 = 54 + 11$

Calculate the sum on both sides of the equation.
$13.0x = 65$

Divide both sides of the equation by $13.0$ to solve for $x$ .
$\frac{13.0x}{13.0} = \frac{65}{13.0}$

Calculate the division on both sides to find the value of $x$ .
$x = 5$
The solution to the equation $8.6x + 4.4x - 11 = 54$ is $x = 5$ .