Questions: Solve the equation by first multiplying both sides through by an appropriate power of 10 so that the equation contains integers only. 7.6x + 6 - 8.6x = 9 x = (Type an integer or a decimal.)

Solve the equation by first multiplying both sides through by an appropriate power of 10 so that the equation contains integers only.
7.6x + 6 - 8.6x = 9
x = (Type an integer or a decimal.)

Transcript text: Solve the equation by first multiplying both sides through by an appropriate power of 10 so that the equation contains integers only. \[ 7.6 x+6-8.6 x=9 \] $\mathrm{x}=$ $\square$ (Type an integer or a decimal.)

Solution

Solution Steps

To solve the equation $7.6x + 6 - 8.6x = 9$, we can first eliminate the decimals by multiplying every term by 10. This will convert the equation into one with integer coefficients. Then, we can combine like terms and solve for $x$.

Step 1: Eliminate Decimals by Multiplying by 10

To eliminate the decimals, multiply every term in the equation $7.6x + 6 - 8.6x = 9$ by 10: \[ 10 \cdot (7.6x + 6 - 8.6x) = 10 \cdot 9 \] This simplifies to: \[ 76x + 60 - 86x = 90 \]

Step 2: Combine Like Terms

Combine the $x$ terms: \[ 76x - 86x + 60 = 90 \] This simplifies to: \[ -10x + 60 = 90 \]

Step 3: Isolate the Variable

Subtract 60 from both sides to isolate the term with $x$: \[ -10x = 90 - 60 \] \[ -10x = 30 \]

Step 4: Solve for $x$

Divide both sides by -10 to solve for $x$: \[ x = \frac{30}{-10} \] \[ x = -3 \]