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Question Solve for xx in the equation −4.8=−x0.3+3.2-4.8 = -\frac{x}{0.3} + 3.2.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation −4.8=−x0.3+3.2-4.8=-\frac{x}{0.3}+3.2.
2. We need to solve for xx.

STEP 2

First, we want to isolate the term containing xx on one side of the equation. To do this, we can subtract 3.23.2 from both sides of the equation.
−4.8−3.2=−x0.3+3.2−3.2-4.8 - 3.2 = -\frac{x}{0.3} + 3.2 - 3.2

STEP 3

Perform the subtraction on the left side of the equation.
−4.8−3.2=−8.0-4.8 - 3.2 = -8.0

STEP 4

The right side simplifies to just the term with xx.
−8.0=−x0.3-8.0 = -\frac{x}{0.3}

STEP 5

To solve for xx, we need to eliminate the fraction. We can do this by multiplying both sides of the equation by 0.30.3.
0.3×−8.0=0.3×−x0.30.3 \times -8.0 = 0.3 \times -\frac{x}{0.3}

STEP 6

Perform the multiplication on the left side of the equation.
0.3×−8.0=−2.40.3 \times -8.0 = -2.4

STEP 7

On the right side, the 0.30.3 in the numerator and denominator cancel each other out, leaving us with −x-x.
−2.4=−x-2.4 = -x

STEP 8

To find the value of xx, we can multiply both sides of the equation by −1-1 to make xx positive.
−1×−2.4=−1×−x-1 \times -2.4 = -1 \times -x

STEP 9

Perform the multiplication on the left side of the equation.
−1×−2.4=2.4-1 \times -2.4 = 2.4

STEP 10

The right side simplifies to xx.
2.4=x2.4 = x
Thus, the solution to the equation −4.8=−x0.3+3.2-4.8=-\frac{x}{0.3}+3.2 is x=2.4x = 2.4.

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