QuestionSolve $4(x+9)=6 x+14$

Studdy Solution

STEP 1

1. The equation $4(x+9) = 6x + 14$ is a linear equation.
2. The goal is to find the value of $x$ that satisfies the equation.
3. The equation involves distributing, combining like terms, and isolating the variable.

STEP 2

1. Distribute the terms on the left side of the equation.
2. Move all terms involving $x$ to one side of the equation.
3. Move constant terms to the other side of the equation.
4. Solve for $x$ .
5. Check the solution by substituting it back into the original equation.

STEP 3

Distribute the $4$ on the left side of the equation:
$4(x+9) = 4 \cdot x + 4 \cdot 9$
This simplifies to:
$4x + 36 = 6x + 14$

STEP 4

Move all terms involving $x$ to one side of the equation. Subtract $4x$ from both sides:
$4x + 36 - 4x = 6x + 14 - 4x$
This simplifies to:
$36 = 2x + 14$

STEP 5

Move constant terms to the other side of the equation. Subtract $14$ from both sides:
$36 - 14 = 2x + 14 - 14$
This simplifies to:
$22 = 2x$

STEP 6

Solve for $x$ by dividing both sides by $2$ :
$\frac{22}{2} = \frac{2x}{2}$
This simplifies to:
$x = 11$

STEP 7

Check the solution by substituting $x = 11$ back into the original equation:
Original equation: $4(x+9) = 6x + 14$
Substitute $x = 11$ :
$4(11+9) = 6(11) + 14$
Simplify both sides:
$4 \cdot 20 = 66 + 14$
$80 = 80$
Both sides are equal, confirming the solution is correct.
The solution is:
$\boxed{11}$

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