Sure, let's solve the equation step by step.
Step 1: Expand the equation inside the brackets
We start with the equation:
[tex]\[ 4[x + 2(3x - 7)] = 22x - 65 \][/tex]
First, simplify the expression inside the brackets:
[tex]\[ 2(3x - 7) \][/tex]
Distribute the 2:
[tex]\[ 2 \cdot 3x - 2 \cdot 7 = 6x - 14 \][/tex]
So, we get:
[tex]\[ x + 6x - 14 = 7x - 14 \][/tex]
Step 2: Substitute back and expand
Now, substituting this back into the original equation:
[tex]\[ 4[7x - 14] = 22x - 65 \][/tex]
Distribute the 4:
[tex]\[ 4 \cdot 7x - 4 \cdot 14 = 28x - 56 \][/tex]
So, the equation becomes:
[tex]\[ 28x - 56 = 22x - 65 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
Isolate the variable [tex]\( x \)[/tex].
First, let's move all [tex]\( x \)[/tex]-terms to one side:
[tex]\[ 28x - 22x = -65 + 56 \][/tex]
Simplify:
[tex]\[ 6x = -9 \][/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-9}{6} = -\frac{3}{2} \][/tex]
Therefore, the solution to the equation [tex]\( 4[x+2(3x-7)] = 22x - 65 \)[/tex] is [tex]\( x = -\frac{3}{2} \)[/tex].
So, the correct answer is:
[tex]\[ -\frac{3}{2} \][/tex]
