Question

5-8|-2x|=-75 can someone show me how to solve this? Like the steps?

Answer 1

No solution

Explanation:

To solve the equation 5-8|-2x|=-75, we can follow these steps:

Step 1: Isolate the Absolute Value

We begin by isolating the absolute value term by adding 8|-2x| to both sides of the equation:

• 5-8|-2x|+8|-2x|=-75+8|-2x|

Simplifying the left side, we get:

• 5=-75+|-16x|

Subtracting 5 from both sides, we get:

• |-16x|=-80

Step 2: Remove the Absolute Value

Since the absolute value of a number is always positive, we can split the equation into two cases:

• -16x=80 or -16x=-80

Step 3: Solve for x

Solving for x in the first case, we get:

• -16x=80
• x=-5

Solving for x in the second case, we get:

• -16x=-80
• x=5

Step 4: Check the Solution

We need to check if the solutions we found satisfy the original equation. Plugging in x=-5, we get:

• 5-8|-2(-5)|=-75
• 5-8|10|=-75
• 5-80=-75 (which is false)

Therefore, x=-5 is not a solution.

Plugging in x=5, we get:

• 5-8|-2(5)|=-75
• 5-8|(-10)|=-75
• 5+80=-75 (which is false)

Therefore, x=5 is also not a solution.

Answer 2

Sure, I can help you solve this equation step by step:

Given equation: 5 - 8|-2x| = -75

Step 1: Remove the absolute value by considering two cases:
Case 1: -2x is positive
Case 2: -2x is negative

Step 2: Solve for Case 1 (when -2x is positive):
5 - 8(-2x) = -75
5 + 16x = -75
16x = -75 - 5
16x = -80
x = -80 / 16
x = -5

Step 3: Solve for Case 2 (when -2x is negative):
5 - 8(2x) = -75
5 - 16x = -75
-16x = -75 - 5
-16x = -80
x = -80 / -16
x = 5

So, the solutions for the equation are x = -5 and x = 5.

You can verify these solutions by substituting them back into the original equation to make sure they satisfy the equation.