|-2x +5|=|5x + 7|

Solve the equation: | -2x + 5 | = | 5x + 7 |

When we have an absolute value equation like this, it means the two expressions inside the absolute value can be equal or opposites.

So, we consider two cases:

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Case 1:

Set the expressions equal:

-2x + 5 = 5x + 7

Let's solve for x:

• Subtract 5x from both sides: -2x - 5x + 5 = 7
• -7x + 5 = 7
• Subtract 5 from both sides: -7x = 2
• Divide both sides by -7: x = 2 / -7
• So, x = -2/7

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Case 2:

Set the expressions equal with opposite signs:

-2x + 5 = - (5x + 7)

which simplifies to:

-2x + 5 = -5x - 7

Let's solve for x:

• Add 5x to both sides: -2x + 5x + 5 = -7
• 3x + 5 = -7
• Subtract 5 from both sides: 3x = -12
• Divide both sides by 3: x = -12 / 3
• So, x = -4

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Final answer:

Solutions are x = -2/7 and x = -4.