SOLUTION: Solve the compound inequality. 7 > -3x + 6 or 8

SOLUTION: Solve the compound inequality. 7 > -3x + 6 or 8 < -3x +4.

Question 250203: Solve the compound inequality.
7 > -3x + 6 or 8 < -3x +4.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
or
Just solve each separate inequality.
Subtracting 6 from each side of the first inequality and 4 from each side of the second we get:
or
Divide each inequality by -3. (Remember that whenever you multiply or divide both sides of an inequality by any negative number, you must reverse the inequality!)
or
These simplify to:
or

When working with inequalities it is important to learn how to read them correctly. In Math we don't always read from left to right like we do in English. With inequalities you should always read inequalities starting from where the variable is.

Both of the inequalities above have the x on the right side. So we should read both of them from right to left! The first one says, when read correctly, "x is greater than -1/3". If we were to graph this one, the shading would start from -1/3 and go to the right because all greater than's go to the right.

The second inequality says "x is less than -4/3" and its graph would start at -4/3 and go to the left because all less than's go to the left.

At -1/3 and -4/3 there would be open circles because there are no "or equal to" inequalities.

Since this is an "or" compound inequality, its graph would be the graphs of both inequalities on the same number line. (Unfortunately Algebra.com's graphing facility does not draw graphs of inequalities. You'll just have to picture an open circle at -1/3 with a shaded arrow to the right and an open circle at -4/3 with a shaded arrow to the left, both of these on the same number line.)
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