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24.If l, m, and n are all parallel, solve for x.x + 51012.8x-3m12A. 11B 13c.15D14

24If L M And N Are All Parallel Solve For Xx 510128x3m12A 11B 13c15D14 class=

Sagot :

SOLUTION

Using the ratio of the parallel sides, we have

[tex]\frac{x+5}{12.8}=\frac{10}{x-3}[/tex]

Simplify by cross multiplying the fraction

[tex]\begin{gathered} (x+5)(x-3)=10\times12.8 \\ x^2-3x+5x-15=128 \\ x^2+2x-15-128=0 \\ x^2+2x-143=0 \end{gathered}[/tex]

The leads to a quadratic equation, which will be solved using the factor method

[tex]x^2+13x-11x-143=0[/tex]

By binomial factors, we have

[tex]\begin{gathered} x(x+13)-11(x+13)=0 \\ (x+13)(x-11)=0 \end{gathered}[/tex]

Then equate each expression to 0, we obtain

[tex]\begin{gathered} x+13=0\text{ 0r X-11=0} \\ x=-13,11 \end{gathered}[/tex]

Therefore x=-13,11

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