Question

select all expressions that are equivalent to this algebraic expression.
(2x-1)-3.25(x+3)
a. 2x-1-3.25x-9.75
b. 2x-3.25x-1-9.75
c. -1.25x-1-9.75
d. -1.25x-10.75
e. 2x-1-3.25x+9.75
f.1.25x+1-.75
g.-1.25x-4

Answer 1

To determine which expressions are equivalent to the original expression \((2x - 1) - 3.25(x + 3)\), we will first simplify the original expression step by step:

1. **Distribute \(-3.25\)** over \((x + 3)\):
\[
-3.25(x + 3) = -3.25x - 9.75
\]

2. **Substitute this back into the expression**:
\[
(2x - 1) - (3.25x + 9.75) = 2x - 1 - 3.25x - 9.75
\]

3. **Combine the like terms**:
- Combine the \(x\) terms:
\[
2x - 3.25x = -1.25x
\]
- Combine the constant terms:
\[
-1 - 9.75 = -10.75
\]

So, the simplified expression is:
\[
-1.25x - 10.75
\]

Now, let's evaluate each of the options given:

a. **\(2x - 1 - 3.25x - 9.75\)**:
- Simplifies to:
\[
-1.25x - 10.75 \quad \text{(Equivalent)}
\]

b. **\(2x - 3.25x - 1 - 9.75\)**:
- Simplifies to:
\[
-1.25x - 10.75 \quad \text{(Equivalent)}
\]

c. **\(-1.25x - 1 - 9.75\)**:
- Simplifies to:
\[
-1.25x - 10.75 \quad \text{(Equivalent)}
\]

d. **\(-1.25x - 10.75\)**:
- Already matches exactly \(-1.25x - 10.75 \quad \text{(Equivalent)}\)

e. **\(2x - 1 - 3.25x + 9.75\)**:
- Simplifies to:
\[
-1.25x + 8.75 \quad \text{(Not equivalent)}
\]

f. **\(1.25x + 1 - .75\)**:
- Simplifies to:
\[
1.25x + 0.25 \quad \text{(Not equivalent)}
\]

g. **\(-1.25x - 4\)**:
- This does not match \(-1.25x - 10.75 \quad \text{(Not equivalent)}\)

**Summary of equivalent expressions**:
- a. \(2x - 1 - 3.25x - 9.75\)
- b. \(2x - 3.25x - 1 - 9.75\)
- c. \(-1.25x - 1 - 9.75\)
- d. \(-1.25x - 10.75\)

Thus, the equivalent expressions are a, b, c, and d.