Question7) $3 x+4(3 x+6)=9$

Studdy Solution

STEP 1

1. The equation $3x + 4(3x + 6) = 9$ is a linear equation in one variable.
2. The equation involves distributing and combining like terms.
3. The goal is to solve for the variable $x$ .

STEP 2

1. Expand the equation by distributing the terms.
2. Combine like terms.
3. Isolate the variable $x$ by performing algebraic operations.
4. Check the solution by substituting it back into the original equation.

STEP 3

First, distribute the $4$ into the terms inside the parentheses:
$4(3x + 6) = 4 \cdot 3x + 4 \cdot 6$
This simplifies to:
$12x + 24$

STEP 4

Substitute the expanded terms back into the original equation:
$3x + 12x + 24 = 9$
Now, combine like terms:
$(3x + 12x) + 24 = 9$
This simplifies to:
$15x + 24 = 9$

STEP 5

Isolate the variable $x$ by first subtracting 24 from both sides of the equation:
$15x + 24 - 24 = 9 - 24$
This simplifies to:
$15x = -15$
Next, divide both sides by 15 to solve for $x$ :
$\frac{15x}{15} = \frac{-15}{15}$
This simplifies to:
$x = -1$

STEP 6

Check the solution by substituting $x = -1$ back into the original equation:
$3(-1) + 4(3(-1) + 6) = 9$
Simplify within the parentheses first:
$3(-1) + 4(-3 + 6) = 9$
$3(-1) + 4(3) = 9$
$-3 + 12 = 9$
Simplify the left-hand side:
$9 = 9$
Both sides are equal, confirming that the solution is correct.
The solution is:
$\boxed{-1}$

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