solve each inequality and graph its solution a. 2x> -12 b. y + 5 _>2 c. x\4 _> -1 d.6z-3-5z<4
a. 2X> -12.
X > -6.
Graph: Open circle at -6 with arrow
pointing rt. The open circle means that
-6 is NOT a part of the solution.
Always use the OPEN circle when there is no equal sign in your inequality.
Solution Set:
b. Y + 5 >= 2.
Y >= 2 - 5,
Y >= -3.
Graph: Closed circle at -3 with arrow
pointing rt. The closed circle means
that -3 is a part of the solution.
The Solution Set: Y = -3, and all values of Y > -3.
a. Solution Set: All values of X > -6.
a. To solve the inequality 2x > -12, we need to find the values of x that satisfy this inequality.
Step 1: Divide both sides of the inequality by 2:
2x/2 > -12/2
This simplifies to:
x > -6
Step 2: Graph the solution on a number line. Since x is greater than -6, we will shade the region to the right of -6 on the number line. A solid dot can be placed on -6 to indicate that it is not included in the solution.
b. To solve the inequality y + 5 ≥ 2, we need to find the values of y that satisfy this inequality.
Step 1: Subtract 5 from both sides of the inequality:
y + 5 - 5 ≥ 2 - 5
This simplifies to:
y ≥ -3
Step 2: Graph the solution on a number line. Since y is greater than or equal to -3, we will shade the region to the right of -3 on the number line. A closed dot can be placed on -3 to indicate that it is included in the solution.
c. To solve the inequality x/4 ≥ -1, we need to find the values of x that satisfy this inequality.
Step 1: Multiply both sides of the inequality by 4 (since we have a denominator of 4):
4 * (x/4) ≥ -1 * 4
This simplifies to:
x ≥ -4
Step 2: Graph the solution on a number line. Since x is greater than or equal to -4, we will shade the region to the right of -4 on the number line. A closed dot can be placed on -4 to indicate that it is included in the solution.
d. To solve the inequality 6z - 3 - 5z < 4, we need to find the values of z that satisfy this inequality.
Step 1: Combine like terms on the left side of the inequality by subtracting 5z:
6z - 5z - 3 < 4
This simplifies to:
z - 3 < 4
Step 2: Add 3 to both sides of the inequality:
z - 3 + 3 < 4 + 3
This simplifies to:
z < 7
Step 3: Graph the solution on a number line. Since z is less than 7, we will shade the region to the left of 7 on the number line. An open dot can be placed on 7 to indicate that it is not included in the solution.