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Simplify 2(3v+9)-14-6(-5v-4)

A. 36v+28
B. 106v+98
C. -6v-13
D. -24v-20

5 answers

To simplify the expression \( 2(3v + 9) - 14 - 6(-5v - 4) \), we will follow the order of operations: distribute, combine like terms, and simplify.

  1. Distribute \( 2 \) in \( 2(3v + 9) \): \[ 2(3v) + 2(9) = 6v + 18 \]

  2. Distribute \( -6 \) in \( -6(-5v - 4) \): \[ -6(-5v) - 6(-4) = 30v + 24 \]

  3. Now substitute these back into the expression: \[ 6v + 18 - 14 + 30v + 24 \]

  4. Combine like terms:

    • Combine the \( v \) terms: \[ 6v + 30v = 36v \]
    • Combine the constant terms: \[ 18 - 14 + 24 = 28 \]

  5. So the simplified expression is: \[ 36v + 28 \]

Thus, the answer is \( \boxed{A} : 36v + 28 \).

-15+4/5(15e-10)-10e.

To simplify the expression \(-15 + \frac{4}{5}(15e - 10) - 10e\), follow these steps:

  1. Distribute \(\frac{4}{5}\) to \((15e - 10)\): \[ \frac{4}{5} \times 15e = 12e \] \[ \frac{4}{5} \times -10 = -8 \]

    So, \(\frac{4}{5}(15e - 10) = 12e - 8\).

  2. Substitute this back into the original expression: \[ -15 + (12e - 8) - 10e \]

  3. Combine the like terms:

    • Combine the \( e \) terms: \[ 12e - 10e = 2e \]
    • Combine the constant terms: \[ -15 - 8 = -23 \]

  4. So the final simplified expression is: \[ 2e - 23 \]

Thus, the answer is \( 2e - 23 \).

Factor 48y-36z using the GCF.

To factor the expression \( 48y - 36z \) using the greatest common factor (GCF), follow these steps:

  1. Determine the GCF of the coefficients:

    • The coefficients are \( 48 \) and \( 36 \).
    • The factors of \( 48 \) are \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \).
    • The factors of \( 36 \) are \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).
    • The common factors are \( 1, 2, 3, 4, 6, 12 \).
    • The greatest common factor is \( 12 \).

  2. Factor out the GCF (which is \( 12 \)): \[ 48y - 36z = 12(4y - 3z) \]

So, the factored form of \( 48y - 36z \) using the GCF is: \[ \boxed{12(4y - 3z)} \]