Here are a few problems I need solving Make sure to show a check for the solution and write the solution in set notation like {x|x>5}:
Solve for y
-7y-14>42
Solve for x
-2(4x+5) < 2x-20
I do not know set notation. When multiplying/dividing both sides of an inequality by a negative, reverse the carat.
-7y > 56
y < -8
-8x + 10 < 2x - 20
-10x < -30
x > 3
I goofed with a sign. It should be:
-8x - 10 < 2x - 20
-10x < -10
x > 1
To solve the equation -7y - 14 > 42, we need to isolate the variable y.
Step 1: Begin by moving the constant term to the other side of the inequality by adding 14 to both sides:
-7y - 14 + 14 > 42 + 14
-7y > 56
Step 2: Next, divide both sides of the inequality by -7. Since we are dividing by a negative number, the inequality sign will flip:
(-7y)/(-7) < 56/(-7)
y < -8
Therefore, the solution to the inequality -7y - 14 > 42 is y < -8.
To write the solution in set notation, we express it as {y | y < -8}.
Now, let's solve the equation -2(4x + 5) < 2x - 20.
Step 1: Begin by distributing -2 to the terms inside the parentheses:
-8x - 10 < 2x - 20
Step 2: Next, move the constant term to the other side of the inequality by adding 10 to both sides:
-8x - 10 + 10 < 2x - 20 + 10
-8x < 2x - 10
Step 3: Combine like terms by bringing all the x terms to one side of the inequality:
-8x - 2x < -10
-10x < -10
Step 4: Divide both sides of the inequality by -10. Since we are dividing by a negative number, the inequality sign will flip:
(-10x)/(-10) > (-10)/(-10)
x > 1
Therefore, the solution to the inequality -2(4x + 5) < 2x - 20 is x > 1.
In set notation, we express it as {x | x > 1}.