Of course! Let's solve the given equation step-by-step. The equation is:
[tex]\[ 16x - [3x - (6 - 9x)] = 30x + [(3x + 2) - (x + 3)] \][/tex]
### Step 1: Simplify inside the brackets
1. Simplify inside the first bracket:
[tex]\[ 3x - (6 - 9x) \][/tex]
Distribute the negative sign inside the bracket:
[tex]\[ 3x - 6 + 9x = 12x - 6 \][/tex]
2. Simplify inside the second bracket:
[tex]\[ (3x + 2) - (x + 3) \][/tex]
Distribute the negative sign inside the bracket:
[tex]\[ 3x + 2 - x - 3 = 2x - 1 \][/tex]
### Step 2: Substitute the simplified expressions back into the equation
[tex]\[ 16x - (12x - 6) = 30x + (2x - 1) \][/tex]
### Step 3: Simplify the equation further
1. On the left-hand side:
[tex]\[ 16x - 12x + 6 = 4x + 6 \][/tex]
2. On the right-hand side:
[tex]\[ 30x + 2x - 1 = 32x - 1 \][/tex]
So the equation now looks like:
[tex]\[ 4x + 6 = 32x - 1 \][/tex]
### Step 4: Isolate the variable [tex]\( x \)[/tex]
1. Move all terms containing [tex]\( x \)[/tex] to one side and constant terms to the other side:
[tex]\[ 4x + 6 = 32x - 1 \][/tex]
Subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 6 = 28x - 1 \][/tex]
2. Add 1 to both sides:
[tex]\[ 7 = 28x \][/tex]
3. Divide both sides by 28 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{7}{28} \][/tex]
### Step 5: Simplify the fraction
[tex]\[ \frac{7}{28} = \frac{1}{4} \][/tex]
Therefore, the solution to the equation is:
[tex]\[ x = \frac{1}{4} \][/tex]
