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in Linear Equations by (15.7k points)

Solve each of the following in equations and represent the solution set on the number line.

\(\frac{5x - 8}{3} \ge \frac{4x - 7}{2}\), Where x ϵ R.

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1 Answer

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by (15.2k points)

Given:

\(\frac{5x - 8}{3}\ge \frac{4x - 7}{2}\), Where x ϵ R.

(5x – 8).(2) ≥ (4x-7).(3) 

10x – 16 ≥ 12x -21 

Now, adding 16 to both the sides 

10x -16 + 16 ≥ 12x -21 + 16 

10x ≥ 12x -5 

Now, subtracting 12x from both the sides of the above equation 

10x -12x ≥ 12x – 5 – 12x 

-2x ≥ -5 

Now, multiplying by -1 on both the sides of above equation 

(-2x)(-1) ≥ (-5)(-1) 

2x ≤ 5 (inequality reversed) 

Therefore,

\(\le\)\(\frac{5}{2}\)

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