1)Solve 3+2(1-x)>6 or 2x+14<=8. Graph the solution set on a number line.
The number line I'm working with is:
-4 -3 -2 -1 0 1
First solution:
3+2-2x>6
5-2x>6
-2x>1
x> -1/2
for the graph, I have an open circle between 0 and 1 and the arrow going right.
Second solution:
2x+14<=8
2x<= -6
x<= -3
for the graph, I have a closed circle on the -3 and the arrow going left.
seem right to me.
You made an error in the first part.
for the first one you had
-2x>1
x> -1/2
when you divide by a negative, the inequality sign has to be reversed, so it is
x < -1/2
so that would be an open circle at -1/2 and the line going to the left.
since your relations are joined with OR and the second one is x < -3
the actual solution would be the first graph above.
To solve the inequality 3+2(1-x)>6, follow these steps:
1. Distribute the 2 to both terms inside the parentheses: 3+2-2x>6.
2. Combine like terms on the left side: 5-2x>6.
3. Subtract 5 from both sides: -2x>1.
4. Divide both sides of the inequality by -2. Since dividing by a negative number flips the inequality, remember to flip the sign: x<-1/2.
To solve the inequality 2x+14<=8, follow these steps:
1. Subtract 14 from both sides: 2x<= -6.
2. Divide both sides of the inequality by 2: x<= -3.
On the number line you provided, mark an open circle at -1/2 (excluding it because the inequality is strictly greater than) and draw an arrow to the right as the solution for the first equation. Mark a closed circle at -3 (including it because the inequality is less than or equal to) and draw an arrow to the left as the solution for the second equation.