Let's solve this problem step-by-step.
STEP-BY-STEP SOLUTION:
First let's write out the inequality that we will be solving.
( 6x - 3 ) / 2 > 37 / 10 + ( x + 2 ) / 5
Then, let's make the denominators the same for each of the fractions by using their HCF ( Highest Common Factor ) which is 10 and multiplying the numerator of each fraction respectively so that they are all over the same denominator which is 10. After that, since they are all over the same denominator, you just have to write the numerator of each fraction without the denominator.
5 ( 6x - 3 ) > 37 + 2 ( x + 2 )
Next we will expand all brackets.
30x - 15 > 37 + 2x + 4
Then we will make ( x ) the subject and solve accordingly.
30x - 2x > 37 + 4 + 15
28x > 56
x > 56 / 28
x > 2
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