Solved on Nov 29, 2023

Find the value of xx in the equation 1.5(x+4)3=4.5(x2)1.5(x+4)-3=4.5(x-2).

STEP 1

Assumptions
1. The equation is 1.5(x+4)3=4.5(x2)1.5(x+4)-3=4.5(x-2)
2. We are solving for the variable xx

STEP 2

First, we will distribute the 1.51.5 on the left side of the equation.
1.5(x+4)3=1.5x+1.5431.5(x+4)-3 = 1.5x + 1.5*4 - 3

STEP 3

Calculate the multiplication.
1.5x+63=1.5x+31.5x + 6 - 3 = 1.5x + 3

STEP 4

Similarly, distribute the 4.54.5 on the right side of the equation.
4.5(x2)=4.5x4.524.5(x-2) = 4.5x - 4.5*2

STEP 5

Calculate the multiplication.
4.5x9=4.5x94.5x - 9 = 4.5x - 9

STEP 6

Now, we have the equation as:
1.5x+3=4.5x91.5x + 3 = 4.5x - 9

STEP 7

Next, we will isolate the variable xx on one side of the equation. Let's start by subtracting 1.5x1.5x from both sides of the equation.
1.5x1.5x+3=4.5x1.5x91.5x - 1.5x + 3 = 4.5x - 1.5x - 9

STEP 8

Simplify the equation.
3=3x93 = 3x - 9

STEP 9

Next, add 99 to both sides of the equation to isolate 3x3x on one side.
3+9=3x9+93 + 9 = 3x - 9 + 9

STEP 10

Simplify the equation.
12=3x12 = 3x

STEP 11

Finally, divide both sides of the equation by 33 to solve for xx.
12/3=3x/312 / 3 = 3x / 3

STEP 12

Calculate the division to find the value of xx.
x=4x = 4
The value of xx in the equation 1.5(x+4)3=4.5(x2)1.5(x+4)-3=4.5(x-2) is 44.

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