Solve for x: 6x + one over four (4x+8) > 12
2 answers:
Answer to Problem:
So this says any number larger than 10/7 is a solution.
A graph to represent the solution:
O~~~~~~~~~~~~~~~~~~~~ x>10/7
---------------------------(10/7)---------------------
Step-by-step explanation:
We are given:
I'm going to distribute first:
Combine like terms:
Subtract 2 on both sides:
Divide both sides by 7:
So this says any number larger than 10/7 is a solution.
A graph to represent the solution:
O~~~~~~~~~~~~~~~~~~~~ x>10/7
---------------------------(10/7)---------------------
I used an open circle because there wasn't a line under the inequality (no line under to represent equals).
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You want to isolate the x-term from the constant term, so you can subtract x/3 and add 10. This gives you
... 4/9x -10 -x/3 +10 > x/3 -12 -x/3 +10
... 1/9x > -2 . . . . . . collect terms
Now, you can multiply by 9 to see the condition on x.
... 9(1/9x) > -2(9)
... x > -18
On the x-y plane, the graph of this will be a dashed line at x=-18, and the half-plane to the right of that line will be shaded.
On a number line, there will be an open circle at x=-18, and the number line to the right of that circle will be marked (bold, colored, shaded, whatever).
