Certainly! Let's solve the given equation step-by-step.
The initial equation is:
[tex]\[ 4(x + 5) = 6(2x - 1) \][/tex]
Step 1: Distribute the numbers on both sides.
On the left side, distribute the [tex]\(4\)[/tex] into the expression inside the parentheses:
[tex]\[ 4(x + 5) = 4x + 20 \][/tex]
On the right side, distribute the [tex]\(6\)[/tex] into the expression inside the parentheses:
[tex]\[ 6(2x - 1) = 12x - 6 \][/tex]
Now the equation looks like this:
[tex]\[ 4x + 20 = 12x - 6 \][/tex]
Step 2: Move all terms involving [tex]\(x\)[/tex] to one side and all constant terms to the other side.
First, subtract [tex]\(4x\)[/tex] from both sides of the equation to start simplifying:
[tex]\[ 4x + 20 - 4x = 12x - 6 - 4x \][/tex]
[tex]\[ 20 = 8x - 6 \][/tex]
Next, add [tex]\(6\)[/tex] to both sides to isolate the term involving [tex]\(x\)[/tex]:
[tex]\[ 20 + 6 = 8x - 6 + 6 \][/tex]
[tex]\[ 26 = 8x \][/tex]
Step 3: Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(8\)[/tex].
[tex]\[ x = \frac{26}{8} \][/tex]
Step 4: Simplify the fraction.
[tex]\[ x = \frac{26}{8} \][/tex]
[tex]\[ x = \frac{13}{4} \][/tex]
So the solution to the equation is:
[tex]\[ x = 3.25 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] is:
[tex]\[ x = 3.25 \][/tex]
