10 - 2 (x + 3) = 3x + 2
What does x equal?
9 answers
To solve the equation \( 10 - 2 (x + 3) = 3x + 2 \), follow these steps:
Distribute the -2 on the left side: \[ 10 - 2x - 6 = 3x + 2 \]
Simplify the left side: \[ 4 - 2x = 3x + 2 \]
To isolate \( x \), first add \( 2x \) to both sides: \[ 4 = 5x + 2 \]
Next, subtract 2 from both sides: \[ 2 = 5x \]
Finally, divide both sides by 5: \[ x = \frac{2}{5} \]
Thus, the solution is: \[ \boxed{\frac{2}{5}} \]
To solve the equation
\[ \frac{3(8x + 24)}{12} = 9 - 3(x - 4), \]
we can start simplifying both sides.
\[ \frac{3(8x + 24)}{12} = \frac{3}{12}(8x + 24) = \frac{1}{4}(8x + 24) = 2x + 6. \]
So the left side becomes:
\[ 2x + 6. \]
Distributing the \(-3\) on the right side gives:
\[ 9 - 3(x - 4) = 9 - 3x + 12 = 21 - 3x. \]
Now we have:
\[ 2x + 6 = 21 - 3x. \]
Add \(3x\) to both sides:
\[ 2x + 3x + 6 = 21 \implies 5x + 6 = 21. \]
Then subtract \(6\) from both sides:
\[ 5x = 15. \]
Finally, divide by \(5\):
\[ x = 3. \]
Thus, the solution is:
\[ \boxed{3}. \]
To simplify the expression \(2 \cdot (3 + 3b)\), we can distribute the \(2\) to both terms inside the parentheses.
Distribute: \[ 2 \cdot 3 + 2 \cdot 3b \]
Calculate: \[ 6 + 6b \]
Thus, the simplified expression is:
\[ \boxed{6 + 6b} \]
To solve the equation
\[ 3(7 + 3b) = 6 + 6b, \]
follow these steps:
Distribute the \(3\) on the left side: \[ 3 \cdot 7 + 3 \cdot 3b = 21 + 9b. \]
So the equation becomes: \[ 21 + 9b = 6 + 6b. \]
Get all terms involving \(b\) on one side of the equation and constant terms on the other side. Subtract \(6b\) from both sides: \[ 21 + 9b - 6b = 6, \] which simplifies to: \[ 21 + 3b = 6. \]
Subtract \(21\) from both sides: \[ 3b = 6 - 21, \] simplifying this gives: \[ 3b = -15. \]
Divide by \(3\) to solve for \(b\): \[ b = \frac{-15}{3} = -5. \]
Thus, the solution is:
\[ \boxed{-5}. \]
To calculate \(-2 \cdot 6\):
\[ -2 \cdot 6 = -12. \]
So, the result is:
\[ \boxed{-12}. \]
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