|y + 4| < 1
A. -5 < y < -3
B. -3 < y < 5
C. -4 < y < 1
D. 1 < y < 4
A
|2t| - 5 = 7
A. t = 1 or -1
B. t = 6 or -6
C. t = 10 or -10
D. t = 12 or -12
B
|a| - 3/4 = -5/8
A. 1/8 or -1/8
B. 7/8 or -7/8
C. 1 3/8 or -1 3/8
D. no solution
A
1. Yep
2. Yep
3. Yep
Arent there 4 questions,, its wtvv
To solve the inequality |y + 4| < 1, we need to isolate y. Here's how you can solve it step-by-step:
Step 1: Remove the absolute value by considering both the positive and negative cases.
Case 1: y + 4 is positive (y + 4 > 0)
In this case, the inequality becomes y + 4 < 1.
Subtract 4 from both sides:
y < 1 - 4
y < -3
Therefore, for the positive case, we have y < -3.
Case 2: y + 4 is negative (y + 4 < 0)
In this case, the inequality becomes -(y + 4) < 1.
Multiply both sides by -1 (which changes the direction of the inequality):
y + 4 > -1
Subtract 4 from both sides:
y > -1 - 4
y > -5
Therefore, for the negative case, we have y > -5.
Step 2: Combine the solutions from both cases.
Since both cases need to be true simultaneously, we can find the intersection of the two solutions.
The intersection of y < -3 and y > -5 is -5 < y < -3.
Therefore, the correct answer is A. -5 < y < -3.
To solve the inequality |y + 4| < 1, we need to isolate the variable y. Let's break it down step by step:
Step 1: Remove the absolute value bars by considering both cases:
Case 1: y + 4 < 1
Case 2: -(y + 4) < 1
Step 2: Solve for y in each case.
Case 1: y + 4 < 1
Subtract 4 from both sides: y < 1 - 4
Simplify: y < -3
Case 2: -(y + 4) < 1
Distribute the negative sign: -y - 4 < 1
Add 4 to both sides: -y < 1 + 4
Simplify: -y < 5
To isolate y, we need to multiply both sides by -1, but since we are multiplying by a negative number, we need to flip the inequality sign.
Multiply both sides by -1 and flip the inequality sign: y > -5
Step 3: Combine the solutions from both cases.
The solution for the inequality |y + 4| < 1 is -5 < y < -3.
Therefore, the correct answer is A. -5 < y < -3.
Now let's move on to the next question.
To solve the equation |2t| - 5 = 7, we need to isolate the variable t. Let's go through the steps:
Step 1: Remove the absolute value bars by considering both cases:
Case 1: 2t - 5 = 7
Case 2: -(2t) - 5 = 7
Step 2: Solve for t in each case.
Case 1: 2t - 5 = 7
Add 5 to both sides: 2t = 7 + 5
Simplify: 2t = 12
Divide both sides by 2: t = 12 / 2
Simplify: t = 6
Case 2: -(2t) - 5 = 7
Add 5 to both sides: -(2t) = 7 + 5
Simplify: -(2t) = 12
Divide both sides by -2: t = 12 / -2
Simplify: t = -6
Step 3: Combine the solutions from both cases.
The solutions for the equation |2t| - 5 = 7 are t = 6 and t = -6.
Therefore, the correct answer is B. t = 6 or -6.
Moving on to the last question.
To solve the equation |a| - 3/4 = -5/8, we need to isolate the variable a. Let's follow the steps:
Step 1: Remove the absolute value bars by considering both cases:
Case 1: a - 3/4 = -5/8
Case 2: -(a) - 3/4 = -5/8
Step 2: Solve for a in each case.
Case 1: a - 3/4 = -5/8
Add 3/4 to both sides: a = -5/8 + 3/4
Get a common denominator: a = -5/8 + 6/8
Combine the fractions: a = 1/8
Case 2: -(a) - 3/4 = -5/8
Add 3/4 to both sides: -(a) = -5/8 + 3/4
Get a common denominator: -(a) = -5/8 + 6/8
Combine the fractions: -(a) = 1/8
To isolate a, we need to multiply both sides by -1, but since we are multiplying by a negative number, we need to flip the inequality sign.
Multiply both sides by -1 and flip the inequality sign: a = -1/8
Step 3: Combine the solutions from both cases.
The solutions for the equation |a| - 3/4 = -5/8 are a = 1/8 and a = -1/8.
Therefore, the correct answer is A. 1/8 or -1/8.