Algebra Math Help

Help with solving and graphing inequalities, Algebra 2?

Solve and Graph
2x > -6 and x – 4 < 3

You have to solve for x so move everything else to the other side. Graph the resulting answers you find as if they were a line so pretend the < and > signs are = signs and graph. Then shade to the corresponding inequality. Also use dash lines as the inequalities don’t include the actual number.

1. 2x > -6 => x > -3 and x – 4 < 3 => x < 7
To graph, simply draw a vertical (up and down) line where x=-3 and x=7. For the first inequality, shade to the right of the line up to x=7 and for the second, shade to the left of the line up to x=-3.

2. x + 3 > 2x + 1 => x < 2 and -4x < -8 => x > 2
Graph a vertical line at x=2 and shade to the left and right of the line.

3. -6 < x + 3 < 6 => -9 < x < 3 (x > -9 and x < 3)
Graph vertical lines at x=-9 and x=3 and shade to the right of x=-9 up to x=3 and shade to the left of x=3 up to x=-9.

4. -3x > -6 => x < 2 or x - 5 < 2 => x < 7
Graph vertical lines at x=2 and x=7. Shade to the left of x=2 and to the left of x=7.

5. x - 2 > 2x + 1 => x < -3 or 10 > -2x + 2 => x > -4
Graph vertical lines at x=-3 and x=-4. Shade to the left of x=-3 and to the right of x=-4.

California Standards Test: Algebra II (Graphing Inequalities