Math

Question Solve the equation 6.8x+9.3=9.4+3.4(25x)6.8x + 9.3 = -9.4 + 3.4(2 - 5x) by distributing, combining terms, and applying properties.

Studdy Solution

STEP 1

Assumptions
1. We are given the equation 6.8x+9.3=9.4+3.4(25x)6.8x + 9.3 = -9.4 + 3.4(2 - 5x).
2. We need to solve for the variable xx.
3. We will use the distributive property to expand terms within parentheses.
4. We will combine like terms where necessary.
5. We will apply the properties of addition, subtraction, multiplication, and division to isolate xx.

STEP 2

First, we will use the distributive property to expand the term 3.4(25x)3.4(2 - 5x).
6.8x+9.3=9.4+3.4×23.4×5x6.8x + 9.3 = -9.4 + 3.4 \times 2 - 3.4 \times 5x

STEP 3

Now, we will multiply the constants by 3.43.4.
6.8x+9.3=9.4+6.817x6.8x + 9.3 = -9.4 + 6.8 - 17x

STEP 4

Next, we will combine the constant terms on the right side of the equation.
6.8x+9.3=2.617x6.8x + 9.3 = -2.6 - 17x

STEP 5

Now, we will add 17x17x to both sides of the equation to combine the xx terms on one side.
6.8x+17x+9.3=2.617x+17x6.8x + 17x + 9.3 = -2.6 - 17x + 17x

STEP 6

Combine the xx terms on the left side of the equation.
23.8x+9.3=2.623.8x + 9.3 = -2.6

STEP 7

Next, we will subtract 9.39.3 from both sides of the equation to isolate the xx term on one side.
23.8x+9.39.3=2.69.323.8x + 9.3 - 9.3 = -2.6 - 9.3

STEP 8

Combine the constant terms on the right side of the equation.
23.8x=11.923.8x = -11.9

STEP 9

Now, we will divide both sides of the equation by 23.823.8 to solve for xx.
23.8x23.8=11.923.8\frac{23.8x}{23.8} = \frac{-11.9}{23.8}

STEP 10

Calculate the value of xx.
x=11.923.8x = \frac{-11.9}{23.8}

STEP 11

Simplify the fraction by dividing both the numerator and the denominator by 11.911.9.
x=11.923.8=12x = \frac{-11.9}{23.8} = \frac{-1}{2}
The solution to the equation is x=12x = -\frac{1}{2}.

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