For what values of x is the following inequality true? 5/7 + x/7 > (underlined) 10. plz ! 12 points

Hello! Thank you for your question! I will be most happy to help!

So here what we are going to do is solve for X.

Step 1: Simplify x/7

Equation at the end of step 1: 5/7 + x/7 - 10 > 0

Step 2: Simplify 5/7

Equation at the end of step 2:

5/7 + x/7 - 10 > 0

Step 3: Adding fractions which have a common denominator: 

3.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5 + x / 7 = x + 5 / 7

Equation at the end of step 3:

(x + 5) / 7 - 10 > 0

Step 4: Rewriting the whole as an Equivalent Fraction:

4.1 Subtracting a whole from a fraction 

Rewrite the whole as a fraction using 7 as the denominator:

10 = 10 / 1 = 10 * 7 / 7

Equivalent fraction: The fraction thus generated looks different but has the same value as the whole 

Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

4.2 Adding up the two equivalent fractions 

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(x+5) - (10 * 7) / 7 = x - 65 / 7

Equation at the end of step 4:

x - 65 / 7 > 0

Step 5: 5.1 Multiply both sides by 7

Solve Basic Inequality: 

5.2 Add  65  to both sides

x > 65

Final  x > 65