Question

solve for x. -15x - 8x - 6x + 16x - 15 = 11 x = \boxed{}

Explanation:

Step1: Combine like terms

Combine the \(x\)-terms: \(-15x - 8x - 6x + 16x\). Calculate the coefficients: \(-15 - 8 - 6 + 16 = -13\)? Wait, no: \(-15 - 8 = -23\), \(-23 - 6 = -29\), \(-29 + 16 = -13\)? Wait, no, let's do it again: \(-15x -8x = -23x\), \(-23x -6x = -29x\), \(-29x +16x = -13x\). Wait, but the equation is \(-15x -8x -6x +16x -15 = 11\)? Wait, the original equation: let's re-express. The user's equation: \(-15x -8x -6x +16x -15 = 11\)? Wait, the image shows: "Solve for x. -15x -8x -6x +16x -15 = 11"? Wait, no, the text: " -15x -8x -6x +16x -15 = 11" and "x = " with a box. Wait, maybe I misread. Let's check again. The equation: \(-15x - 8x - 6x + 16x - 15 = 11\)? Wait, no, the user's image: "Solve for x. -15x -8x -6x +16x -15 = 11" and "x = " [box]. Wait, let's combine the x-terms:

\(-15x -8x -6x +16x = (-15 -8 -6 +16)x = (-29 +16)x = -13x\). Then the equation is \(-13x -15 = 11\).

Step2: Add 15 to both sides

Add 15 to both sides: \(-13x -15 +15 = 11 +15\) → \(-13x = 26\).

Step3: Divide by -13

Divide both sides by -13: \(x = \frac{26}{-13} = -2\). Wait, let's check again. Wait, maybe the original equation is \(-15x -8x -6x +16x -15 = 11\)? Wait, no, maybe the constant term is on the other side. Wait, the user's image: " -15x -8x -6x +16x -15 = 11" → let's re-express:

Combine x-terms: \(-15x -8x -6x +16x = (-15 -8 -6 +16)x = (-29 +16)x = -13x\). So equation: \(-13x -15 = 11\).

Add 15 to both sides: \(-13x = 11 +15 = 26\).

Divide by -13: \(x = 26 / (-13) = -2\).

Wait, let's verify. Plug x = -2 into the original left side:

\(-15(-2) -8(-2) -6(-2) +16(-2) -15\)

Calculate each term:

-15*(-2) = 30

-8*(-2) = 16

-6*(-2) = 12

16*(-2) = -32

So sum: 30 +16 +12 -32 -15 = (30+16+12) - (32+15) = 58 - 47 = 11. Which matches the right side. So x = -2.

Wait, maybe I made a mistake in combining terms. Let's recheck the x-terms:

-15x -8x = -23x

-23x -6x = -29x

-29x +16x = -13x. Correct. Then -13x -15 = 11. Add 15: -13x = 26. Divide by -13: x = -2. Correct.

Answer:

\(x = -2\)