Question 100719
Begin with {{{7(x-3)>5x-14}}}.

To solve, you can start with the equivalent equation:

{{{7(x-3)=5x-14}}}

Multiplying to remove the parentheses:

{{{7x-21=5x-14}}}

Subtracting 5x from both sides:

{{{2x-21>-14}}}

Adding 21 to both sides:

{{{2x=7}}}, so

{{{x=7/2}}}, which may be stated as {{{x=3.5}}} if you wanted.

Now we return to the original inequality, and see that our answer is {{{x>7/2}}}.

Returning to the original equation, we can check a few values.

Check {{{7(x-3)>5x-14}}}, where x = 3. This results in the assertion 0 > 1, which is false. So the value x = 3 does not work, as we expect.

Check {{{7(x-3)>5x-14}}}, where x = 4. This results in the assertion 7 > 6, which is true, as we expected given we think the solution is x > 7/2.

Check {{{7(x-3)>5x-14}}}, where x = 2. This results in the assertion -7 > -4, which is false. So the value x = 2 does not work, as we expect.

Check {{{7(x-3)>5x-14}}}, where x = 5. This results in the assertion 14 > 9, which is true. So the value x = 5 works, as we expect.

{{{graph(x>7/2)}}}