Question

Expand -3(2a - 5)
*
-6a - 15
-6a - 5
9a
-6a + 15

Answer 1

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

Answer 2

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 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:

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