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The original equation is:
[tex]\[ \frac{8}{9}(54x - 36) + 2 = -\frac{3}{4}(-40 + 16x) + 90x \][/tex]

Solve for [tex]\( x \)[/tex]:

[tex]\[ \frac{8}{9}(54x - 36) + 2 = -\frac{3}{4}(-40 + 16x) + 90x \][/tex]

Enter your answer in the box:
[tex]\[ x = 2(9g + 7) \quad 3(9g - 13) \][/tex]

Note: The final answer provided seems nonsensical. It should be clarified or corrected, but without additional context or instructions, this part is left as-is.


Sagot :

Certainly! Let's solve the equation step-by-step:

[tex]\[ \frac{8}{9}(54x - 36) + 2 = -\frac{3}{4}(-40 + 16x) + 90x \][/tex]

First, we distribute the constants inside the parentheses:

On the left-hand side:
[tex]\[ \frac{8}{9}(54x - 36) \][/tex]
Multiply inside the parentheses:
[tex]\[ \frac{8}{9} \cdot 54x - \frac{8}{9} \cdot 36 = 48x - 32 \][/tex]

So the left-hand side becomes:
[tex]\[ 48x - 32 + 2 = 48x - 30 \][/tex]

Now, on the right-hand side:
[tex]\[ -\frac{3}{4}(-40 + 16x) \][/tex]
Distribute the constant inside the parentheses:
[tex]\[ -\frac{3}{4} \cdot (-40) + \frac{3}{4} \cdot 16x = 30 + 12x \][/tex]

So the right-hand side becomes:
[tex]\[ 30 + 12x + 90x = 30 + 102x \][/tex]

Now we have the equation:
[tex]\[ 48x - 30 = 30 + 102x \][/tex]

To solve for [tex]\(x\)[/tex], we first get all terms involving [tex]\(x\)[/tex] on one side and constants on the other side. Subtract [tex]\(48x\)[/tex] from both sides:
[tex]\[ -30 = 30 + 54x \][/tex]

Then, subtract 30 from both sides:
[tex]\[ -60 = 54x \][/tex]

Solve for [tex]\(x\)[/tex] by dividing both sides by 54:
[tex]\[ x = \frac{-60}{54} = -\frac{10}{9} \][/tex]

So the solution is:
[tex]\[ x = -\frac{10}{9} \][/tex]