Expand -3(2a - 5)

Question

*
-6a - 15
-6a - 5
9a
-6a + 15

Answer 1

To expand the expression \(-3(2a - 5)\), you will distribute \(-3\) to both terms inside the parentheses.

Here's the step-by-step expansion:

\[ -3(2a - 5) = -3 \cdot 2a + -3 \cdot (-5) \]

Calculating each term:

1. \(-3 \cdot 2a = -6a\)
2. \(-3 \cdot (-5) = 15\)

Putting it all together:

\[ -3(2a - 5) = -6a + 15 \]

So the expanded form is:

Answer: \(-6a + 15\)

This matches one of the options you provided.

Answer 2

Subtract the expression. Use fractions in the final form.1/3(z+ 2/5) -4 ( 1/2z -2)

Answer 3

To subtract the expression \( \frac{1}{3}(z + \frac{2}{5}) - 4\left(\frac{1}{2}z - 2\right) \), we'll start by distributing both terms inside the parentheses and then simplify.

Step 1: Distribute the first term

\[ \frac{1}{3}(z + \frac{2}{5}) = \frac{1}{3}z + \frac{1}{3} \cdot \frac{2}{5} = \frac{1}{3}z + \frac{2}{15} \]

Step 2: Distribute the second term

\[ -4\left(\frac{1}{2}z - 2\right) = -4 \cdot \frac{1}{2}z + 4 \cdot 2 = -2z + 8 \]

Step 3: Combine the results

Combining the two results we have:

\[ \frac{1}{3}z + \frac{2}{15} - 2z + 8 \]

Step 4: Combine like terms

Next, let's group the \( z \) terms together and the constant terms together:

1. For the \( z \) terms: \[ \frac{1}{3}z - 2z = \frac{1}{3}z - \frac{6}{3}z = \frac{1 - 6}{3}z = -\frac{5}{3}z \]

2. For the constant terms: \[ \frac{2}{15} + 8 = \frac{2}{15} + \frac{120}{15} = \frac{2 + 120}{15} = \frac{122}{15} \]

Final Answer

Combining both parts, we get:

\[ -\frac{5}{3}z + \frac{122}{15} \]

So, the final simplified expression is:

\[ \boxed{-\frac{5}{3}z + \frac{122}{15}} \]