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Solve for x

: −4(2x−11)+7=19
. (1 point)
Responses

x=4
x is equal to 4 - no response given

x=−4
x is equal to negative 4 - incorrect

x=2
x is equal to 2 - no response given

x=−2

1 answer

To solve the equation \(-4(2x−11) + 7 = 19\), follow these steps:

  1. Distribute the \(-4\) on the left side: \[ -4 \cdot 2x + 4 \cdot 11 + 7 = 19 \] This simplifies to: \[ -8x + 44 + 7 = 19 \]

  2. Combine like terms: \[ -8x + 51 = 19 \]

  3. Subtract \(51\) from both sides: \[ -8x = 19 - 51 \] This simplifies to: \[ -8x = -32 \]

  4. Divide both sides by \(-8\): \[ x = \frac{-32}{-8} \] This simplifies to: \[ x = 4 \]

Thus, the solution is \(x = 4\).