Equations are used to represent equal expressions.
The value of x in [tex]\frac{x + 4}{x + 9} = \frac 65[/tex] is -34
The equation is given as:
[tex]\frac{x + 4}{x + 9} = \frac 65[/tex]
Cross multiply
[tex]5 \times (x + 4) = 6 \times (x + 9)[/tex]
Apply distributive properties
[tex]5 \times x + 5 \times 4 = 6 \times x + 6 \times 9[/tex]
Evaluate all products
[tex]5x + 20= 6x + 54[/tex]
Collect like terms
[tex]6x - 5x = 20 - 54[/tex]
[tex]x = -34[/tex]
Hence, the value of x is -34.
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