Solving an inequality with one variable simply means isolating the variable and simplifying.
First perform the operations required on each side
7 - 4y + 4 > -y + 7
11 - 4y > -y + 7
Now isolate the variable, this time by adding y - 11 to each side
-3y > -4
Now simplify so that your equation features y rather than a coefficient times y. Note that in this case, because the coefficient is less than one, the inequality sign must change direction.
y < 4/3
graphing an inequality is done by first noting whether it is a pure inequality (< or >) or a mixed inequality (≤ or ≥).
Pure inequalities are graphed using dashed lines because the boundary line itself is not part of the solution set. Mixed inequalities are graphed using a solid line because the boundary line is part of the solution.
Second, figure out the boundary equation, which is the equality between the two expressions of your inequality,
y = 4/3
Since your inequality is pure in this example, graph y= 4/3 using a dashed line. That is the boundary between values in your solution set and values that are not solutions.
Finally, you need to shade in the half-plane that includes your solution set. For linear inequalities it is usually easy to figure that out without too much trouble, but take one simple step and you will never shade the wrong part of the graph no matter how difficult the equation.
Take a point that is easy to calculate, the origin (0,0) is usually the easiest, and figure out if it is in the solution set; (0) < 4/3 is true therefore the origin is in the solution set and everything on that side of the boundary (that half-plane) is in the solution set. If the boundary goes through the origin, pick some point that is easy to calculate, (0,1) and (1,0) come to mind, and that is clearly not on the boundary and use that test. If your test point satisfies the inequality then the half-plane it resides in is your solution set; if your test point fails to satisfy the inequality, the other half plane is the solution set.
Determine: pure (dashed) or mixed (solid)
Solve for the boundary equation
Graph the boundary equation using dashed or solid lines as appropriate
Test a convenient value
Shade in the solution set.
