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

Studdy Solution

STEP 1

Assumptions
1. The equation to solve is 8.6x+4.4x−11=548.6x + 4.4x - 11 = 54.
2. We need to find the value of xx.

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)x

STEP 3

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

STEP 4

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

STEP 5

Add 1111 to both sides of the equation to isolate the term with the variable xx on one side.
13.0x−11+11=54+1113.0x - 11 + 11 = 54 + 11

STEP 6

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

STEP 7

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

STEP 8

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

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