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The original expression appears to be incorrectly formatted and contains errors. Let's rewrite it to make sense:

Solve the equation:
[tex]\[ 18\left(\frac{4x + 3x - 6}{1} = \frac{8x}{1} \cdot \frac{5(2x - 4)}{18}\right) \][/tex]

If that doesn't make sense, a simplified form might be intended:
[tex]\[ 18 \left( \frac{4x + 3x - 6}{1} \right) = \frac{8x}{1} \cdot \frac{5(2x - 4)}{18} \][/tex]

To ensure clarity, verify the intended equation format from the source.

Sagot :

GinnyAnsweridn
Let's solve the equation step by step. The given equation is:

[tex]\[18\left[\frac{4x + 3x - 6}{1} = \frac{8x}{1} + \frac{5(2x - 4)}{18}\right].\][/tex]

Simplify inside the brackets first:

[tex]\[ \frac{4x + 3x - 6}{1} = 4x + 3x - 6 = 7x - 6. \][/tex]

Next, look at the right-hand side of the equation:

[tex]\[ \frac{8x}{1} = 8x. \][/tex]

And simplify the fraction:

[tex]\[ \frac{5(2x - 4)}{18}. \][/tex]

First, distribute the 5 across [tex]\(2x - 4\)[/tex]:

[tex]\[ 5(2x - 4) = 10x - 20. \][/tex]

Then, we have:

[tex]\[ \frac{10x - 20}{18}. \][/tex]

We can simplify [tex]\(\frac{10x - 20}{18}\)[/tex] further. Factor out a 2 from the numerator:

[tex]\[ \frac{10x - 20}{18} = \frac{2(5x - 10)}{18} = \frac{5x - 10}{9}. \][/tex]

Now substitute back into the equation:

[tex]\[ 18\left[7x - 6 = 8x + \frac{5x - 10}{9}\right]. \][/tex]

To clear the fraction, multiply every term by 18:

[tex]\[ 18(7x - 6) = 18\left(8x + \frac{5x - 10}{9}\right). \][/tex]

Distribute the 18:

[tex]\[ 18(7x - 6) = 126x - 108. \][/tex]

And for the right-hand side:

[tex]\[ 18 \left(8x + \frac{5x - 10}{9}\right) = 18 \cdot 8x + 18 \cdot \frac{5x - 10}{9}. \][/tex]

Simplify inside the parentheses:

[tex]\[ 18 \cdot 8x = 144x, \][/tex]

and

[tex]\[ 18 \cdot \frac{5x - 10}{9} = 2(5x - 10) = 10x - 20. \][/tex]

So the equation becomes:

[tex]\[ 126x - 108 = 144x + 10x - 20. \][/tex]

Simplify the right-hand side:

[tex]\[ 126x - 108 = 154x - 20. \][/tex]

Move all terms involving [tex]\(x\)[/tex] on one side and constants on the other side:

[tex]\[ 126x - 154x = -20 + 108, \][/tex]

[tex]\[ -28x = 88. \][/tex]

Finally, solve for [tex]\(x\)[/tex]:

[tex]\[ x = \frac{88}{-28} = -\frac{22}{7}. \][/tex]

So the solution to the given equation is:

[tex]\[ x = -\frac{22}{7}. \][/tex]
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