NayaL509022 NayaL509022
  • 03-11-2022
  • Mathematics
contestada

Solve for X. Write down what type of solution the equation has. 3) [tex] \frac{10}{2x + 1} = \frac{14}{4x - 7} [/tex]

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CasimirG29866 CasimirG29866
  • 03-11-2022

You have the following equation:

[tex]\frac{10}{2x+1}=\frac{14}{4x-7}[/tex]

In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):

[tex]\begin{gathered} (2x+1)(4x-7)\frac{10}{2x+1}=(2x+1)(4x-7)\frac{14}{4x-7} \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=\frac{84}{12} \\ x=7 \end{gathered}[/tex]

Hence, the solution to the given equation is x = 7

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