Question

2|v-7|+11=41 If there is more than one solution If there is no solution, click on

Answer 1

To solve the equation 2|v-7|+11=41, isolate the absolute value expression and then solve for v. The solutions are v = 22 or v = -8.

Step-by-step explanation:

To solve the equation 2|v-7|+11=41, we need to isolate the absolute value expression and then solve for v. First, subtract 11 from both sides of the equation: 2|v-7|=30. Next, divide both sides by 2 to get |v-7|=15. Since the absolute value of a number is equal to either the number itself or its negative, we can set up two separate equations to find the solutions:

v-7=15 or v-7=-15

Solving each equation gives us two possible values for v: v=22 or v=-8

Answer 2

The equation '|2v - 7| + 11 = 41 has one solution. Option B is answer.

Step-by-step explanation:

Isolate the absolute value term:

Subtract 11 from both sides: |2v - 7| = 30.

Consider the two cases within the absolute value:

Case 1: 2v - 7 ≥ 0:

This means 2v ≥ 7, so v ≥ 7/2. Solving this inequality gives v ≥ 3.5.

Case 2: 2v - 7 < 0:

Multiplying both sides by -1, we get -2v + 7 ≥ 0, which implies -2v ≥ -7, so v ≤ 7/2. Solving this inequality gives v ≤ 3.5.

Combine the solutions:

Both cases lead to the same range of possible values for v: 3.5 ≤ v ≤ 7/2. This means there is only one solution for v that satisfies the original equation.

Therefore, the equation has one solution. Option B is answer.

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Complete Question:

Identify the number of solutions the equation '|2v - 7| + 11 = 41 ' has.

Two Solutions

One Solution

No Solution

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